Model predictive maintenance system with financial analysis functionality

ABSTRACT

A model predictive maintenance system for building equipment. The system includes one or more processing circuits including one or more processors and memory storing instructions that, when executed by the one or more processors, cause the one or more processors to perform operations. The operations include performing an optimization of an objective function that defines a present value of a total cost of operating the building equipment and performing maintenance on the building equipment as a function of operating decisions and maintenance decisions for the building equipment for time steps within a time period. The total cost includes one or more costs incurred during one or more future time steps of the time period. The operations include operating the building equipment and performing maintenance on the building equipment in accordance with decisions defined by the result of the optimization.

CROSS-REFERENCE TO RELATED PATENT APPLICATIONS

This application is a continuation-in-part of U.S. patent applicationSer. No. 16/457,314 filed Jun. 28, 2019, which is a continuation-in-partof U.S. patent application Ser. No. 15/895,836 filed Feb. 13, 2018,which claims the benefit of and priority to U.S. Provisional PatentApplication No. 62/511,113 filed May 25, 2017, the entire disclosures ofwhich are incorporated by reference herein. This application is also acontinuation-in-part of U.S. patent application Ser. No. 15/426,962filed Feb. 7, 2017, the entire disclosure of which is incorporated byreference herein.

BACKGROUND

The present disclosure relates generally to a maintenance system forbuilding equipment and more particularly to a maintenance system thatuses a predictive optimization technique to determine an optimalmaintenance strategy for the building equipment.

Building equipment is typically maintained according to a maintenancestrategy for the building equipment. One type of maintenance strategy isrun-to-fail. The run-to-fail strategy allows the building equipment torun until a failure occurs. During this running period, only minoroperational maintenance tasks (e.g., oil changes) are performed tomaintain the building equipment.

Another type of maintenance strategy is preventative maintenance. Thepreventative maintenance strategy typically involves performing a set ofpreventative maintenance tasks recommended by the equipmentmanufactured. The preventative maintenance tasks are usually performedat regular intervals (e.g., every month, every year, etc.) which may bea function of the elapsed time of operation and/or the run hours of thebuilding equipment.

SUMMARY

One implementation of the present disclosure is a model predictivemaintenance system for building equipment, according to someembodiments. The system includes one or more processing circuitsincluding one or more processors and memory storing instructions that,when executed by the one or more processors, cause the one or moreprocessors to perform operations, according to some embodiments. Theoperations include performing an optimization of an objective functionthat defines a present value of a total cost of operating the buildingequipment and performing maintenance on the building equipment as afunction of operating decisions and maintenance decisions for thebuilding equipment for time steps within a time period, according tosome embodiments. The total cost includes one or more costs incurredduring one or more future time steps of the time period, according tosome embodiments. The operations include operating the buildingequipment and performing maintenance on the building equipment inaccordance with decisions defined by a result of the optimization,according to some embodiments.

In some embodiments, the objective function defines the present value asa function of a constant interest rate for the time steps within thetime period.

In some embodiments, the objective function defines the present value asa function of an interest rate that varies over the time period.

In some embodiments, the objective function further defines a secondpresent value of a total cost of replacing the building equipment as afunction of replacement decisions for the building equipment for thetime steps within the time period. The total cost of replacing thebuilding equipment includes a cost of replacing the building equipmentincurred during a future time step of the time period, according to someembodiments.

In some embodiments, the objective function further defines a risk costassociated with a failure risk of the building equipment at the timesteps of the time period. The risk cost is determined based on adegradation model of the building equipment, according to someembodiments.

In some embodiments, the present value is a net present value ofoperating and maintaining the building equipment over the time period.The optimization is performed to minimize the net present value,according to some embodiments.

In some embodiments, the operations further include updating the presentvalue based on closed-loop feedback of the building equipment. Theclosed-loop feedback of the building equipment is used to update atleast one of an efficiency of the building equipment or a reliability ofthe building equipment, according to some embodiments. The optimizationis performed based on the efficiency of the building equipment and thereliability of the building equipment, according to some embodiments.

Another implementation of the present disclosure is a method forperforming model predictive maintenance of building equipment, accordingto some embodiments. The method includes performing an optimization ofan objective function that defines a present value of a total cost ofoperating the building equipment and performing maintenance on thebuilding equipment as a function of operating decisions and maintenancedecisions for the building equipment for time steps within a timeperiod, according to some embodiments. The total cost includes one ormore costs incurred during one or more future time steps of the timeperiod, according to some embodiments. The method includes operating thebuilding equipment and performing maintenance on the building equipmentin accordance with decisions defined by a result of the optimization,according to some embodiments.

In some embodiments, the objective function defines the present value asa function of a constant interest rate for the time steps within thetime period.

In some embodiments, the objective function defines the present value asa function of an interest rate that varies over the time period.

In some embodiments, the objective function further defines a secondpresent value of a total cost of replacing the building equipment as afunction of replacement decisions for the building equipment for thetime steps within the time period. The total cost of replacing thebuilding equipment includes a cost of replacing the building equipmentincurred during a future time step of the time period, according to someembodiments.

In some embodiments, the objective function further defines a risk costassociated with a failure risk of the building equipment at the timesteps of the time period. The risk cost is determined based on adegradation model of the building equipment, according to someembodiments.

In some embodiments, the present value is a net present value ofoperating and maintaining the building equipment over the time period.The optimization is performed to minimize the net present value,according to some embodiments.

In some embodiments, the method includes updating the present valuebased on closed-loop feedback of the building equipment. The closed-loopfeedback of the building equipment used to update at least one of anefficiency of the building equipment or a reliability of the buildingequipment, according to some embodiments. The optimization is performedbased on the efficiency of the building equipment and the reliability ofthe building equipment, according to some embodiments.

Another implementation of the present disclosure is a controller forperforming model predictive maintenance of building equipment, accordingto some embodiments. The controller includes one or more processors,according to some embodiments. The controller includes one or morenon-transitory computer-readable media storing instructions that, whenexecuted by the one or more processors, cause the one or more processorsto perform operations, according to some embodiments. The operationsinclude performing an optimization of an objective function that definesa present value of a total cost of operating the building equipment andperforming maintenance on the building equipment as a function ofoperating decisions and maintenance decisions for the building equipmentfor time steps within a time period, according to some embodiments. Thetotal cost includes one or more costs incurred during one or more futuretime steps of the time period, according to some embodiments. Theoperations include operating the building equipment and performingmaintenance on the building equipment in accordance with decisionsdefined by a result of the optimization, according to some embodiments.

In some embodiments, the objective function defines the present value asa function of a constant interest rate for the time steps within thetime period.

In some embodiments, the objective function defines the present value asa function of an interest rate that varies over the time period.

In some embodiments, the objective function further defines a secondpresent value of a total cost of replacing the building equipment as afunction of replacement decisions for the building equipment for thetime steps within the time period. The total cost of replacing thebuilding equipment includes a cost of replacing the building equipmentincurred during a future time step of the time period, according to someembodiments.

In some embodiments, the objective function further defines a risk costassociated with a failure risk of the building equipment at the timesteps of the time period. The risk cost is determined based on adegradation model of the building equipment, according to someembodiments.

In some embodiments, the present value is a net present value ofoperating and maintaining the building equipment over the time period.The optimization is performed to minimize the net present value,according to some embodiments.

Those skilled in the art will appreciate that the summary isillustrative only and is not intended to be in any way limiting. Otheraspects, inventive features, and advantages of the devices and/orprocesses described herein, as defined solely by the claims, will becomeapparent in the detailed description set forth herein and taken inconjunction with the accompanying drawings.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a drawing of a building equipped with a HVAC system, accordingto some embodiments embodiment.

FIG. 2 is a block diagram of a waterside system which can be used toserve the heating or cooling loads of the building of FIG. 1 , accordingto some embodiments.

FIG. 3 is a block diagram of an airside system which can be used toserve the heating or cooling loads of the building of FIG. 1 , accordingto some embodiments.

FIG. 4 is a block diagram of a building management system (BMS) whichcan be used to monitor and control the building of FIG. 1 , according tosome embodiments.

FIG. 5 is a block diagram of another BMS which can be used to monitorand control the building of FIG. 1 , according to some embodiments.

FIG. 6 is a block diagram of a building system including a modelpredictive maintenance (MPM) system that monitors equipment performanceinformation from connected equipment installed in the building,according to some embodiments.

FIG. 7 is a schematic diagram of a chiller which may be a type ofconnected equipment that provides equipment performance information tothe MPM system of FIG. 6 , according to some embodiments.

FIG. 8 is a block diagram illustrating the MPM system of FIG. 6 ingreater detail, according to some embodiments.

FIG. 9 is a block diagram illustrating a high level optimizer of the MPMsystem of FIG. 6 in greater detail, according to some embodiments.

FIG. 10 is a flowchart of a process for operating the MPM system of FIG.6 , according to some embodiments.

FIG. 11 is a block diagram of the MPM system of FIG. 8 in greaterdetail, according to some embodiments.

FIG. 12 is a block diagram further illustrating the high level optimizerof FIG. 9 , according to some embodiments.

FIG. 13 is a graph illustrating differences in a total predicted cost ofperforming a maintenance activity on building equipment due to aninterest rate, according to some embodiments.

FIG. 14 is a flow diagram of a process for generating an optimalmaintenance and replacement strategy for building equipment thataccounts for interest rates, according to some embodiments.

DETAILED DESCRIPTION Overview

Referring generally to the FIGURES, a model predictive maintenance (MPM)system and components thereof are shown, according to various exemplaryembodiments. The MPM system can be configured to determine an optimalmaintenance strategy for building equipment. In some embodiments, theoptimal maintenance strategy is a set of decisions which optimizes thetotal cost associated with purchasing, maintaining, and operating thebuilding equipment over the duration of an optimization period (e.g., 30weeks, 52 weeks, 10 years, 30 years, etc.). The decisions can include,for example, equipment purchase decisions, equipment maintenancedecisions, and equipment operating decisions. The MPM system can use amodel predictive control technique to formulate an objective functionwhich expresses the total cost as a function of these decisions, whichcan be included as decision variables in the objective function. The MPMsystem can optimize (e.g., minimize) the objective function using any ofa variety of optimization techniques to identify the optimal values foreach of the decision variables.

One example of an objective function which can be optimized by The MPMsystem is shown in the following equation:

$J = {{\sum\limits_{i = 1}^{h}{C_{{op},i}P_{{op},i}{\Delta t}}} + {\sum\limits_{i = 1}^{h}{C_{{main},i}B_{{main},i}}} + {\sum\limits_{i = 1}^{h}{C_{{cap},i}P_{{cap},i}}}}$where C_(op,i) is the cost per unit of energy (e.g., $/kWh) consumed bythe building equipment at time step i of the optimization period,P_(op,i) is the power consumption (e.g., kW) of the building equipmentat time step i, Δt is the duration of each time step i, C_(main,i) isthe cost of maintenance performed on the building equipment at time stepi, B_(main,i) is a binary variable that indicates whether themaintenance is performed, C_(cap,i) is the capital cost of purchasing anew device of the building equipment at time step i, B_(cap,i) is abinary variable that indicates whether the new device is purchased, andh is the duration of the horizon or optimization period over which theoptimization is performed.

The first term in the objective function J represents the operating costof the building equipment over the duration of the optimization period.In some embodiments, the cost per unit of energy C_(op,i) is receivedfrom a utility as energy pricing data. The cost C_(op,i) may be atime-varying cost that depends on the time of day, the day of the week(e.g., weekday vs. weekend), the current season (e.g., summer vs.winter), or other time-based factors. For example, the cost C_(op,i) maybe higher during peak energy consumption periods and lower duringoff-peak or partial-peak energy consumption periods.

In some embodiments, the power consumption P_(op,i) is based on theheating or cooling load of the building. The heating or cooling load canbe predicted by the MPM system as a function of building occupancy, thetime of day, the day of the week, the current season, or other factorsthat can affect the heating or cooling load. In some embodiments, theMPM system uses weather forecasts from a weather service to predict theheating or cooling load. The power consumption P_(op,i) may also dependon the efficiency η_(i) of the building equipment. For example, buildingequipment that operate at a high efficiency may consume less powerP_(op,i) to satisfy the same heating or cooling load relative tobuilding equipment that operate at a low efficiency.

Advantageously, the MPM system can model the efficiency η_(i) of thebuilding equipment at each time step i as a function of the maintenancedecisions B_(main,i) and the equipment purchase decisions B_(cap,i). Forexample, the efficiency η_(i) for a particular device may start at aninitial value η₀ when the device is purchased and may degrade over timesuch that the efficiency η_(i) decreases with each successive time stepi. Performing maintenance on a device may reset the efficiency η_(i) toa higher value immediately after the maintenance is performed.Similarly, purchasing a new device to replace an existing device mayreset the efficiency η_(i) to a higher value immediately after the newdevice is purchased. After being reset, the efficiency η_(i) maycontinue to degrade over time until the next time at which maintenanceis performed or a new device is purchased.

Performing maintenance or purchasing a new device may result in arelatively lower power consumption P_(op,i) during operation andtherefore a lower operating cost at each time step i after themaintenance is performed or the new device is purchased. In other words,performing maintenance or purchasing a new device may decrease theoperating cost represented by the first term of the objective functionJ. However, performing maintenance may increase the second term of theobjective function J and purchasing a new device may increase the thirdterm of the objective function J. The objective function J captures eachof these costs and can be optimized by the MPM system to determine theoptimal set of maintenance and equipment purchase decisions (i.e.,optimal values for the binary decision variables B_(main,i) andB_(cap,i)) over the duration of the optimization period.

In some embodiments, the MPM system uses equipment performanceinformation received as a feedback from the building equipment toestimate the efficiency and/or the reliability of the buildingequipment. The efficiency may indicate a relationship between theheating or cooling load on the building equipment and the powerconsumption of the building equipment. The MPM system can use theefficiency to calculate the corresponding value of P_(op,i). Thereliability may be a statistical measure of the likelihood that thebuilding equipment will continue operating without fault under itscurrent operating conditions. Operating under more strenuous conditions(e.g., high load, high temperatures, etc.) may result in a lowerreliability, whereas operating under less strenuous conditions (e.g.,low load, moderate temperatures, etc.) may result in a higherreliability. In some embodiments, the reliability is based on an amountof time that has elapsed since the building equipment last receivedmaintenance and/or an amount of time that has elapsed since the buildingequipment was purchased or installed.

In some embodiments, the MPM system generates and provides equipmentpurchase and maintenance recommendations. The equipment purchase andmaintenance recommendations may be based on the optimal values for thebinary decision variables B_(main,i) and B_(cap,i) determined byoptimizing the objective function J. For example, a value ofB_(main,25)=1 for a particular device of the building equipment mayindicate that maintenance should be performed on that device at the25^(th) time step of the optimization period, whereas a value ofB_(main,25)=0 may indicate that the maintenance should not be performedat that time step. Similarly, a value of B_(cap,25)=1 may indicate thata new device of the building equipment should be purchased at the25^(th) time step of the optimization period, whereas a value ofB_(cap,25)=0 may indicate that the new device should not be purchased atthat time step.

Advantageously, the equipment purchase and maintenance recommendationsgenerated by the MPM system are predictive recommendations based on theactual operating conditions and actual performance of the buildingequipment. The optimization performed by the MPM system weighs the costof performing maintenance and the cost of purchasing new equipmentagainst the decrease in operating cost resulting from such maintenanceor purchase decisions in order to determine the optimal maintenancestrategy that minimizes the total combined cost J. In this way, theequipment purchase and maintenance recommendations generated by the MPMsystem may be specific to each group of building equipment in order toachieve the optimal cost J for that specific group of buildingequipment. The equipment-specific recommendations may result in a loweroverall cost J relative to generic preventative maintenancerecommendations provided by an equipment manufacturer (e.g., serviceequipment every year) which may be sub-optimal for some groups ofbuilding equipment and/or some operating conditions.

For estimations made by the MPM system to be accurate, the MPM systemaccount for a time value of money if estimating various costs. The timevalue of money can refer to how a value of money (and/or another cost)can change over time. For example, if a 5% interest rate is estimatedover a next year, $1.00 at a current time can be worth $1.05 at the nextyear due to a decrease in value of money. The value of money canincrease/decrease for a variety of reasons. As a few examples, the valueof money may increase/decrease due to changing federal interest rates,inflation/deflation, etc.

Interest rates can be incorporated with the objective function Joptimized by the MPM system. An example of the objective function Joptimized by the MPM system without interest rates can be shown by thefollowing equation:

${J\left( m_{k} \right)} = {\sum\limits_{k = 1}^{h}\left\{ {{c_{{op},k}\left( \delta_{k} \right)} + {\begin{bmatrix}c_{{main},k} \\c_{{replace},k}\end{bmatrix}^{T}m_{k}} + {c_{{fail},k}^{T}{p_{{fail},k}\left( \delta_{k} \right)}}} \right\}}$where c_(op,k)(δ_(k)) is an operational cost dependent on a state ofdegradation δ_(k), c_(main,k) is a cost of maintenance at a time step kof a horizon or an optimization period, C_(place,k) is a cost ofmaintenance at a time step k of the horizon or optimization period,m_(k) is a binary vector representing which maintenance actions aretaken at time step k, p_(fail,k)(δ_(k)) is a vector of probabilities offailure for each tracked component of the system during the time step kand dependent on the degradation state δ_(k), and c_(fail,k) is a vectorof costs of failure for each of the tracked components of the system.The probability of failure p_(fail,k)(δ_(k)) can be multiplied by thecosts of failure c_(fail,k) (repair cost and opportunity cost) to form arisk term in the cost function.

The objective function J shown above can be augmented to include a timecost of money at each time step k of the optimization period. Forexample, the MPM system can optimize the following objective function J:

${J\left( m_{k} \right)} = {\sum\limits_{k = 1}^{h}{a_{k}\left\{ {{c_{{op},k}\left( \delta_{k} \right)} + {\begin{bmatrix}c_{{main},k} \\c_{{replace},k}\end{bmatrix}^{T}m_{k}} + {c_{{fail},k}^{T}{p_{{fail},k}\left( \delta_{k} \right)}}} \right\}}}$where a_(k) is a time cost of money at time step k. In particular, a_(k)can be given by the following:a _(k)=(1+r)^(−k)where r is an interest rate. As shown, a_(k) can assume a constantinterest rate such that the interest rate does not change over thehorizon or optimization period. However, a time-varying interest ratecan be used to calculate a_(k). Specifically, a_(k) with time-varyinginterest rates can be given by the following:

$a_{k} = {\frac{1}{1 + r_{1}} \times \frac{1}{1 + r_{2}} \times \ldots \times \frac{1}{1 + r_{k}}}$where r_(i) is an interest rate at a time step i such that i≤k. In otherwords, a_(k) with time-varying interest rates can be calculated as aproduct of each interest rate for each time step through time step k. Inthis case, a_(k) can be provided for each time step during theoptimization period based on interest rates from a first time stepthrough time step k.

Advantageously, integration of the interest rate into the objectivefunction J can be independent of what optimization method (e.g., integerprogramming, mixed integer linear programming, stochastic optimization,convex programming, dynamic programming, etc.) is used. In this way, theinterest rates can be captured in the objective function J without aneed for separate implementation dependent on an optimization methodused. These and other features of the MPM system are described in detailbelow.

Building HVAC Systems and Building Management Systems

Referring now to FIGS. 1-5 , several building management systems (BMS)and HVAC systems in which the systems and methods of the presentdisclosure can be implemented are shown, according to some embodiments.In brief overview, FIG. 1 shows a building 10 equipped with a HVACsystem 100. FIG. 2 is a block diagram of a waterside system 200 whichcan be used to serve building 10. FIG. 3 is a block diagram of anairside system 300 which can be used to serve building 10. FIG. 4 is ablock diagram of a BMS which can be used to monitor and control building10. FIG. 5 is a block diagram of another BMS which can be used tomonitor and control building 10.

Building and HVAC System

Referring particularly to FIG. 1 , a perspective view of a building 10is shown. Building 10 is served by a BMS. A BMS is, in general, a systemof devices configured to control, monitor, and manage equipment in oraround a building or building area. A BMS can include, for example, aHVAC system, a security system, a lighting system, a fire alertingsystem, any other system that is capable of managing building functionsor devices, or any combination thereof.

The BMS that serves building 10 includes a HVAC system 100. HVAC system100 can include a plurality of HVAC devices (e.g., heaters, chillers,air handling units, pumps, fans, thermal energy storage, etc.)configured to provide heating, cooling, ventilation, or other servicesfor building 10. For example, HVAC system 100 is shown to include awaterside system 120 and an airside system 130. Waterside system 120 mayprovide a heated or chilled fluid to an air handling unit of airsidesystem 130. Airside system 130 may use the heated or chilled fluid toheat or cool an airflow provided to building 10. An exemplary watersidesystem and airside system which can be used in HVAC system 100 aredescribed in greater detail with reference to FIGS. 2-3 .

HVAC system 100 is shown to include a chiller 102, a boiler 104, and arooftop air handling unit (AHU) 106. Waterside system 120 may use boiler104 and chiller 102 to heat or cool a working fluid (e.g., water,glycol, etc.) and may circulate the working fluid to AHU 106. In variousembodiments, the HVAC devices of waterside system 120 can be located inor around building 10 (as shown in FIG. 1 ) or at an offsite locationsuch as a central plant (e.g., a chiller plant, a steam plant, a heatplant, etc.). The working fluid can be heated in boiler 104 or cooled inchiller 102, depending on whether heating or cooling is required inbuilding 10. Boiler 104 may add heat to the circulated fluid, forexample, by burning a combustible material (e.g., natural gas) or usingan electric heating element. Chiller 102 may place the circulated fluidin a heat exchange relationship with another fluid (e.g., a refrigerant)in a heat exchanger (e.g., an evaporator) to absorb heat from thecirculated fluid. The working fluid from chiller 102 and/or boiler 104can be transported to AHU 106 via piping 108.

AHU 106 may place the working fluid in a heat exchange relationship withan airflow passing through AHU 106 (e.g., via one or more stages ofcooling coils and/or heating coils). The airflow can be, for example,outside air, return air from within building 10, or a combination ofboth. AHU 106 may transfer heat between the airflow and the workingfluid to provide heating or cooling for the airflow. For example, AHU106 can include one or more fans or blowers configured to pass theairflow over or through a heat exchanger containing the working fluid.The working fluid may then return to chiller 102 or boiler 104 viapiping 110.

Airside system 130 may deliver the airflow supplied by AHU 106 (i.e.,the supply airflow) to building 10 via air supply ducts 112 and mayprovide return air from building 10 to AHU 106 via air return ducts 114.In some embodiments, airside system 130 includes multiple variable airvolume (VAV) units 116. For example, airside system 130 is shown toinclude a separate VAV unit 116 on each floor or zone of building 10.VAV units 116 can include dampers or other flow control elements thatcan be operated to control an amount of the supply airflow provided toindividual zones of building 10. In other embodiments, airside system130 delivers the supply airflow into one or more zones of building 10(e.g., via supply ducts 112) without using intermediate VAV units 116 orother flow control elements. AHU 106 can include various sensors (e.g.,temperature sensors, pressure sensors, etc.) configured to measureattributes of the supply airflow. AHU 106 may receive input from sensorslocated within AHU 106 and/or within the building zone and may adjustthe flow rate, temperature, or other attributes of the supply airflowthrough AHU 106 to achieve setpoint conditions for the building zone.

Waterside System

Referring now to FIG. 2 , a block diagram of a waterside system 200 isshown, according to some embodiments. In various embodiments, watersidesystem 200 may supplement or replace waterside system 120 in HVAC system100 or can be implemented separate from HVAC system 100. Whenimplemented in HVAC system 100, waterside system 200 can include asubset of the HVAC devices in HVAC system 100 (e.g., boiler 104, chiller102, pumps, valves, etc.) and may operate to supply a heated or chilledfluid to AHU 106. The HVAC devices of waterside system 200 can belocated within building 10 (e.g., as components of waterside system 120)or at an offsite location such as a central plant.

In FIG. 2 , waterside system 200 is shown as a central plant having aplurality of subplants 202-212. Subplants 202-212 are shown to include aheater subplant 202, a heat recovery chiller subplant 204, a chillersubplant 206, a cooling tower subplant 208, a hot thermal energy storage(TES) subplant 210, and a cold thermal energy storage (TES) subplant212. Subplants 202-212 consume resources (e.g., water, natural gas,electricity, etc.) from utilities to serve thermal energy loads (e.g.,hot water, cold water, heating, cooling, etc.) of a building or campus.For example, heater subplant 202 can be configured to heat water in ahot water loop 214 that circulates the hot water between heater subplant202 and building 10. Chiller subplant 206 can be configured to chillwater in a cold water loop 216 that circulates the cold water betweenchiller subplant 206 building 10. Heat recovery chiller subplant 204 canbe configured to transfer heat from cold water loop 216 to hot waterloop 214 to provide additional heating for the hot water and additionalcooling for the cold water. Condenser water loop 218 may absorb heatfrom the cold water in chiller subplant 206 and reject the absorbed heatin cooling tower subplant 208 or transfer the absorbed heat to hot waterloop 214. Hot TES subplant 210 and cold TES subplant 212 may store hotand cold thermal energy, respectively, for subsequent use.

Hot water loop 214 and cold water loop 216 may deliver the heated and/orchilled water to air handlers located on the rooftop of building 10(e.g., AHU 106) or to individual floors or zones of building 10 (e.g.,VAV units 116). The air handlers push air past heat exchangers (e.g.,heating coils or cooling coils) through which the water flows to provideheating or cooling for the air. The heated or cooled air can bedelivered to individual zones of building 10 to serve thermal energyloads of building 10. The water then returns to subplants 202-212 toreceive further heating or cooling.

Although subplants 202-212 are shown and described as heating andcooling water for circulation to a building, it is understood that anyother type of working fluid (e.g., glycol, CO2, etc.) can be used inplace of or in addition to water to serve thermal energy loads. In otherembodiments, subplants 202-212 may provide heating and/or coolingdirectly to the building or campus without requiring an intermediateheat transfer fluid. These and other variations to waterside system 200are within the teachings of the present disclosure.

Each of subplants 202-212 can include a variety of equipment configuredto facilitate the functions of the subplant. For example, heatersubplant 202 is shown to include a plurality of heating elements 220(e.g., boilers, electric heaters, etc.) configured to add heat to thehot water in hot water loop 214. Heater subplant 202 is also shown toinclude several pumps 222 and 224 configured to circulate the hot waterin hot water loop 214 and to control the flow rate of the hot waterthrough individual heating elements 220. Chiller subplant 206 is shownto include a plurality of chillers 232 configured to remove heat fromthe cold water in cold water loop 216. Chiller subplant 206 is alsoshown to include several pumps 234 and 236 configured to circulate thecold water in cold water loop 216 and to control the flow rate of thecold water through individual chillers 232.

Heat recovery chiller subplant 204 is shown to include a plurality ofheat recovery heat exchangers 226 (e.g., refrigeration circuits)configured to transfer heat from cold water loop 216 to hot water loop214. Heat recovery chiller subplant 204 is also shown to include severalpumps 228 and 230 configured to circulate the hot water and/or coldwater through heat recovery heat exchangers 226 and to control the flowrate of the water through individual heat recovery heat exchangers 226.Cooling tower subplant 208 is shown to include a plurality of coolingtowers 238 configured to remove heat from the condenser water incondenser water loop 218. Cooling tower subplant 208 is also shown toinclude several pumps 240 configured to circulate the condenser water incondenser water loop 218 and to control the flow rate of the condenserwater through individual cooling towers 238.

Hot TES subplant 210 is shown to include a hot TES tank 242 configuredto store the hot water for later use. Hot TES subplant 210 may alsoinclude one or more pumps or valves configured to control the flow rateof the hot water into or out of hot TES tank 242. Cold TES subplant 212is shown to include cold TES tanks 244 configured to store the coldwater for later use. Cold TES subplant 212 may also include one or morepumps or valves configured to control the flow rate of the cold waterinto or out of cold TES tanks 244.

In some embodiments, one or more of the pumps in waterside system 200(e.g., pumps 222, 224, 228, 230, 234, 236, and/or 240) or pipelines inwaterside system 200 include an isolation valve associated therewith.Isolation valves can be integrated with the pumps or positioned upstreamor downstream of the pumps to control the fluid flows in watersidesystem 200. In various embodiments, waterside system 200 can includemore, fewer, or different types of devices and/or subplants based on theparticular configuration of waterside system 200 and the types of loadsserved by waterside system 200.

Airside System

Referring now to FIG. 3 , a block diagram of an airside system 300 isshown, according to some embodiments. In various embodiments, airsidesystem 300 may supplement or replace airside system 130 in HVAC system100 or can be implemented separate from HVAC system 100. Whenimplemented in HVAC system 100, airside system 300 can include a subsetof the HVAC devices in HVAC system 100 (e.g., AHU 106, VAV units 116,ducts 112-114, fans, dampers, etc.) and can be located in or aroundbuilding 10. Airside system 300 may operate to heat or cool an airflowprovided to building 10 using a heated or chilled fluid provided bywaterside system 200.

In FIG. 3 , airside system 300 is shown to include an economizer-typeair handling unit (AHU) 302. Economizer-type AHUs vary the amount ofoutside air and return air used by the air handling unit for heating orcooling. For example, AHU 302 may receive return air 304 from buildingzone 306 via return air duct 308 and may deliver supply air 310 tobuilding zone 306 via supply air duct 312. In some embodiments, AHU 302is a rooftop unit located on the roof of building 10 (e.g., AHU 106 asshown in FIG. 1 ) or otherwise positioned to receive both return air 304and outside air 314. AHU 302 can be configured to operate exhaust airdamper 316, mixing damper 318, and outside air damper 320 to control anamount of outside air 314 and return air 304 that combine to form supplyair 310. Any return air 304 that does not pass through mixing damper 318can be exhausted from AHU 302 through exhaust damper 316 as exhaust air322.

Each of dampers 316-320 can be operated by an actuator. For example,exhaust air damper 316 can be operated by actuator 324, mixing damper318 can be operated by actuator 326, and outside air damper 320 can beoperated by actuator 328. Actuators 324-328 may communicate with an AHUcontroller 330 via a communications link 332. Actuators 324-328 mayreceive control signals from AHU controller 330 and may provide feedbacksignals to AHU controller 330. Feedback signals can include, forexample, an indication of a current actuator or damper position, anamount of torque or force exerted by the actuator, diagnosticinformation (e.g., results of diagnostic tests performed by actuators324-328), status information, commissioning information, configurationsettings, calibration data, and/or other types of information or datathat can be collected, stored, or used by actuators 324-328. AHUcontroller 330 can be an economizer controller configured to use one ormore control algorithms (e.g., state-based algorithms, extremum seekingcontrol (ESC) algorithms, proportional-integral (PI) control algorithms,proportional-integral-derivative (PID) control algorithms, modelpredictive control (MPC) algorithms, feedback control algorithms, etc.)to control actuators 324-328.

Still referring to FIG. 3 , AHU 302 is shown to include a cooling coil334, a heating coil 336, and a fan 338 positioned within supply air duct312. Fan 338 can be configured to force supply air 310 through coolingcoil 334 and/or heating coil 336 and provide supply air 310 to buildingzone 306. AHU controller 330 may communicate with fan 338 viacommunications link 340 to control a flow rate of supply air 310. Insome embodiments, AHU controller 330 controls an amount of heating orcooling applied to supply air 310 by modulating a speed of fan 338.

Cooling coil 334 may receive a chilled fluid from waterside system 200(e.g., from cold water loop 216) via piping 342 and may return thechilled fluid to waterside system 200 via piping 344. Valve 346 can bepositioned along piping 342 or piping 344 to control a flow rate of thechilled fluid through cooling coil 334. In some embodiments, coolingcoil 334 includes multiple stages of cooling coils that can beindependently activated and deactivated (e.g., by AHU controller 330, byBMS controller 366, etc.) to modulate an amount of cooling applied tosupply air 310.

Heating coil 336 may receive a heated fluid from waterside system 200(e.g., from hot water loop 214) via piping 348 and may return the heatedfluid to waterside system 200 via piping 350. Valve 352 can bepositioned along piping 348 or piping 350 to control a flow rate of theheated fluid through heating coil 336. In some embodiments, heating coil336 includes multiple stages of heating coils that can be independentlyactivated and deactivated (e.g., by AHU controller 330, by BMScontroller 366, etc.) to modulate an amount of heating applied to supplyair 310.

Each of valves 346 and 352 can be controlled by an actuator. Forexample, valve 346 can be controlled by actuator 354 and valve 352 canbe controlled by actuator 356. Actuators 354-356 may communicate withAHU controller 330 via communications links 358-360. Actuators 354-356may receive control signals from AHU controller 330 and may providefeedback signals to controller 330. In some embodiments, AHU controller330 receives a measurement of the supply air temperature from atemperature sensor 362 positioned in supply air duct 312 (e.g.,downstream of cooling coil 334 and/or heating coil 336). AHU controller330 may also receive a measurement of the temperature of building zone306 from a temperature sensor 364 located in building zone 306.

In some embodiments, AHU controller 330 operates valves 346 and 352 viaactuators 354-356 to modulate an amount of heating or cooling providedto supply air 310 (e.g., to achieve a setpoint temperature for supplyair 310 or to maintain the temperature of supply air 310 within asetpoint temperature range). The positions of valves 346 and 352 affectthe amount of heating or cooling provided to supply air 310 by coolingcoil 334 or heating coil 336 and may correlate with the amount of energyconsumed to achieve a desired supply air temperature. AHU 330 maycontrol the temperature of supply air 310 and/or building zone 306 byactivating or deactivating coils 334-336, adjusting a speed of fan 338,or a combination of both.

Still referring to FIG. 3 , airside system 300 is shown to include abuilding management system (BMS) controller 366 and a client device 368.BMS controller 366 can include one or more computer systems (e.g.,servers, supervisory controllers, subsystem controllers, etc.) thatserve as system level controllers, application or data servers, headnodes, or master controllers for airside system 300, waterside system200, HVAC system 100, and/or other controllable systems that servebuilding 10. BMS controller 366 may communicate with multiple downstreambuilding systems or subsystems (e.g., HVAC system 100, a securitysystem, a lighting system, waterside system 200, etc.) via acommunications link 370 according to like or disparate protocols (e.g.,LON, BACnet, etc.). In various embodiments, AHU controller 330 and BMScontroller 366 can be separate (as shown in FIG. 3 ) or integrated. Inan integrated implementation, AHU controller 330 can be a softwaremodule configured for execution by a processor of BMS controller 366.

In some embodiments, AHU controller 330 receives information from BMScontroller 366 (e.g., commands, setpoints, operating boundaries, etc.)and provides information to BMS controller 366 (e.g., temperaturemeasurements, valve or actuator positions, operating statuses,diagnostics, etc.). For example, AHU controller 330 may provide BMScontroller 366 with temperature measurements from temperature sensors362-364, equipment on/off states, equipment operating capacities, and/orany other information that can be used by BMS controller 366 to monitoror control a variable state or condition within building zone 306.

Client device 368 can include one or more human-machine interfaces orclient interfaces (e.g., graphical user interfaces, reportinginterfaces, text-based computer interfaces, client-facing web services,web servers that provide pages to web clients, etc.) for controlling,viewing, or otherwise interacting with HVAC system 100, its subsystems,and/or devices. Client device 368 can be a computer workstation, aclient terminal, a remote or local interface, or any other type of userinterface device. Client device 368 can be a stationary terminal or amobile device. For example, client device 368 can be a desktop computer,a computer server with a user interface, a laptop computer, a tablet, asmartphone, a PDA, or any other type of mobile or non-mobile device.Client device 368 may communicate with BMS controller 366 and/or AHUcontroller 330 via communications link 372.

Building Management Systems

Referring now to FIG. 4 , a block diagram of a building managementsystem (BMS) 400 is shown, according to some embodiments. BMS 400 can beimplemented in building 10 to automatically monitor and control variousbuilding functions. BMS 400 is shown to include BMS controller 366 and aplurality of building subsystems 428. Building subsystems 428 are shownto include a building electrical subsystem 434, an informationcommunication technology (ICT) subsystem 436, a security subsystem 438,a HVAC subsystem 440, a lighting subsystem 442, a lift/escalatorssubsystem 432, and a fire safety subsystem 430. In various embodiments,building subsystems 428 can include fewer, additional, or alternativesubsystems. For example, building subsystems 428 may also oralternatively include a refrigeration subsystem, an advertising orsignage subsystem, a cooking subsystem, a vending subsystem, a printeror copy service subsystem, or any other type of building subsystem thatuses controllable equipment and/or sensors to monitor or controlbuilding 10. In some embodiments, building subsystems 428 includewaterside system 200 and/or airside system 300, as described withreference to FIGS. 2-3 .

Each of building subsystems 428 can include any number of devices,controllers, and connections for completing its individual functions andcontrol activities. HVAC subsystem 440 can include many of the samecomponents as HVAC system 100, as described with reference to FIGS. 1-3. For example, HVAC subsystem 440 can include a chiller, a boiler, anynumber of air handling units, economizers, field controllers,supervisory controllers, actuators, temperature sensors, and otherdevices for controlling the temperature, humidity, airflow, or othervariable conditions within building 10. Lighting subsystem 442 caninclude any number of light fixtures, ballasts, lighting sensors,dimmers, or other devices configured to controllably adjust the amountof light provided to a building space. Security subsystem 438 caninclude occupancy sensors, video surveillance cameras, digital videorecorders, video processing servers, intrusion detection devices, accesscontrol devices and servers, or other security-related devices.

Still referring to FIG. 4 , BMS controller 366 is shown to include acommunications interface 407 and a BMS interface 409. Interface 407 mayfacilitate communications between BMS controller 366 and externalapplications (e.g., monitoring and reporting applications 422,enterprise control applications 426, remote systems and applications444, applications residing on client devices 448, etc.) for allowinguser control, monitoring, and adjustment to BMS controller 366 and/orsubsystems 428. Interface 407 may also facilitate communications betweenBMS controller 366 and client devices 448. BMS interface 409 mayfacilitate communications between BMS controller 366 and buildingsubsystems 428 (e.g., HVAC, lighting security, lifts, powerdistribution, business, etc.).

Interfaces 407, 409 can be or include wired or wireless communicationsinterfaces (e.g., jacks, antennas, transmitters, receivers,transceivers, wire terminals, etc.) for conducting data communicationswith building subsystems 428 or other external systems or devices. Invarious embodiments, communications via interfaces 407, 409 can bedirect (e.g., local wired or wireless communications) or via acommunications network 446 (e.g., a WAN, the Internet, a cellularnetwork, etc.). For example, interfaces 407, 409 can include an Ethernetcard and port for sending and receiving data via an Ethernet-basedcommunications link or network. In another example, interfaces 407, 409can include a Wi-Fi transceiver for communicating via a wirelesscommunications network. In another example, one or both of interfaces407, 409 can include cellular or mobile phone communicationstransceivers. In one embodiment, communications interface 407 is a powerline communications interface and BMS interface 409 is an Ethernetinterface. In other embodiments, both communications interface 407 andBMS interface 409 are Ethernet interfaces or are the same Ethernetinterface.

Still referring to FIG. 4 , BMS controller 366 is shown to include aprocessing circuit 404 including a processor 406 and memory 408.Processing circuit 404 can be communicably connected to BMS interface409 and/or communications interface 407 such that processing circuit 404and the various components thereof can send and receive data viainterfaces 407, 409. Processor 406 can be implemented as a generalpurpose processor, an application specific integrated circuit (ASIC),one or more field programmable gate arrays (FPGAs), a group ofprocessing components, or other suitable electronic processingcomponents.

Memory 408 (e.g., memory, memory unit, storage device, etc.) can includeone or more devices (e.g., RAM, ROM, Flash memory, hard disk storage,etc.) for storing data and/or computer code for completing orfacilitating the various processes, layers and modules described in thepresent application. Memory 408 can be or include volatile memory ornon-volatile memory. Memory 408 can include database components, objectcode components, script components, or any other type of informationstructure for supporting the various activities and informationstructures described in the present application. According to someembodiments, memory 408 is communicably connected to processor 406 viaprocessing circuit 404 and includes computer code for executing (e.g.,by processing circuit 404 and/or processor 406) one or more processesdescribed herein.

In some embodiments, BMS controller 366 is implemented within a singlecomputer (e.g., one server, one housing, etc.). In various otherembodiments BMS controller 366 can be distributed across multipleservers or computers (e.g., that can exist in distributed locations).Further, while FIG. 4 shows applications 422 and 426 as existing outsideof BMS controller 366, in some embodiments, applications 422 and 426 canbe hosted within BMS controller 366 (e.g., within memory 408).

Still referring to FIG. 4 , memory 408 is shown to include an enterpriseintegration layer 410, an automated measurement and validation (AM&V)layer 412, a demand response (DR) layer 414, a fault detection anddiagnostics (FDD) layer 416, an integrated control layer 418, and abuilding subsystem integration later 420. Layers 410-420 can beconfigured to receive inputs from building subsystems 428 and other datasources, determine optimal control actions for building subsystems 428based on the inputs, generate control signals based on the optimalcontrol actions, and provide the generated control signals to buildingsubsystems 428. The following paragraphs describe some of the generalfunctions performed by each of layers 410-420 in BMS 400.

Enterprise integration layer 410 can be configured to serve clients orlocal applications with information and services to support a variety ofenterprise-level applications. For example, enterprise controlapplications 426 can be configured to provide subsystem-spanning controlto a graphical user interface (GUI) or to any number of enterprise-levelbusiness applications (e.g., accounting systems, user identificationsystems, etc.). Enterprise control applications 426 may also oralternatively be configured to provide configuration GUIs forconfiguring BMS controller 366. In yet other embodiments, enterprisecontrol applications 426 can work with layers 410-420 to optimizebuilding performance (e.g., efficiency, energy use, comfort, or safety)based on inputs received at interface 407 and/or BMS interface 409.

Building subsystem integration layer 420 can be configured to managecommunications between BMS controller 366 and building subsystems 428.For example, building subsystem integration layer 420 may receive sensordata and input signals from building subsystems 428 and provide outputdata and control signals to building subsystems 428. Building subsystemintegration layer 420 may also be configured to manage communicationsbetween building subsystems 428. Building subsystem integration layer420 translate communications (e.g., sensor data, input signals, outputsignals, etc.) across a plurality of multi-vendor/multi-protocolsystems.

Demand response layer 414 can be configured to optimize resource usage(e.g., electricity use, natural gas use, water use, etc.) and/or themonetary cost of such resource usage in response to satisfy the demandof building 10. The optimization can be based on time-of-use prices,curtailment signals, energy availability, or other data received fromutility providers, distributed energy generation systems 424, fromenergy storage 427 (e.g., hot TES 242, cold TES 244, etc.), or fromother sources. Demand response layer 414 may receive inputs from otherlayers of BMS controller 366 (e.g., building subsystem integration layer420, integrated control layer 418, etc.). The inputs received from otherlayers can include environmental or sensor inputs such as temperature,carbon dioxide levels, relative humidity levels, air quality sensoroutputs, occupancy sensor outputs, room schedules, and the like. Theinputs may also include inputs such as electrical use (e.g., expressedin kWh), thermal load measurements, pricing information, projectedpricing, smoothed pricing, curtailment signals from utilities, and thelike.

According to some embodiments, demand response layer 414 includescontrol logic for responding to the data and signals it receives. Theseresponses can include communicating with the control algorithms inintegrated control layer 418, changing control strategies, changingsetpoints, or activating/deactivating building equipment or subsystemsin a controlled manner. Demand response layer 414 may also includecontrol logic configured to determine when to utilize stored energy. Forexample, demand response layer 414 may determine to begin using energyfrom energy storage 427 just prior to the beginning of a peak use hour.

In some embodiments, demand response layer 414 includes a control moduleconfigured to actively initiate control actions (e.g., automaticallychanging setpoints) which minimize energy costs based on one or moreinputs representative of or based on demand (e.g., price, a curtailmentsignal, a demand level, etc.). In some embodiments, demand responselayer 414 uses equipment models to determine an optimal set of controlactions. The equipment models can include, for example, thermodynamicmodels describing the inputs, outputs, and/or functions performed byvarious sets of building equipment. Equipment models may representcollections of building equipment (e.g., subplants, chiller arrays,etc.) or individual devices (e.g., individual chillers, heaters, pumps,etc.).

Demand response layer 414 may further include or draw upon one or moredemand response policy definitions (e.g., databases, XML files, etc.).The policy definitions can be edited or adjusted by a user (e.g., via agraphical user interface) so that the control actions initiated inresponse to demand inputs can be tailored for the user's application,desired comfort level, particular building equipment, or based on otherconcerns. For example, the demand response policy definitions canspecify which equipment can be turned on or off in response toparticular demand inputs, how long a system or piece of equipment shouldbe turned off, what setpoints can be changed, what the allowable setpoint adjustment range is, how long to hold a high demand setpointbefore returning to a normally scheduled setpoint, how close to approachcapacity limits, which equipment modes to utilize, the energy transferrates (e.g., the maximum rate, an alarm rate, other rate boundaryinformation, etc.) into and out of energy storage devices (e.g., thermalstorage tanks, battery banks, etc.), and when to dispatch on-sitegeneration of energy (e.g., via fuel cells, a motor generator set,etc.).

Integrated control layer 418 can be configured to use the data input oroutput of building subsystem integration layer 420 and/or demandresponse later 414 to make control decisions. Due to the subsystemintegration provided by building subsystem integration layer 420,integrated control layer 418 can integrate control activities of thesubsystems 428 such that the subsystems 428 behave as a singleintegrated supersystem. In some embodiments, integrated control layer418 includes control logic that uses inputs and outputs from a pluralityof building subsystems to provide greater comfort and energy savingsrelative to the comfort and energy savings that separate subsystemscould provide alone. For example, integrated control layer 418 can beconfigured to use an input from a first subsystem to make anenergy-saving control decision for a second subsystem. Results of thesedecisions can be communicated back to building subsystem integrationlayer 420.

Integrated control layer 418 is shown to be logically below demandresponse layer 414. Integrated control layer 418 can be configured toenhance the effectiveness of demand response layer 414 by enablingbuilding subsystems 428 and their respective control loops to becontrolled in coordination with demand response layer 414. Thisconfiguration may advantageously reduce disruptive demand responsebehavior relative to conventional systems. For example, integratedcontrol layer 418 can be configured to assure that a demandresponse-driven upward adjustment to the setpoint for chilled watertemperature (or another component that directly or indirectly affectstemperature) does not result in an increase in fan energy (or otherenergy used to cool a space) that would result in greater total buildingenergy use than was saved at the chiller.

Integrated control layer 418 can be configured to provide feedback todemand response layer 414 so that demand response layer 414 checks thatconstraints (e.g., temperature, lighting levels, etc.) are properlymaintained even while demanded load shedding is in progress. Theconstraints may also include setpoint or sensed boundaries relating tosafety, equipment operating limits and performance, comfort, fire codes,electrical codes, energy codes, and the like. Integrated control layer418 is also logically below fault detection and diagnostics layer 416and automated measurement and validation layer 412. Integrated controllayer 418 can be configured to provide calculated inputs (e.g.,aggregations) to these higher levels based on outputs from more than onebuilding subsystem.

Automated measurement and validation (AM&V) layer 412 can be configuredto verify that control strategies commanded by integrated control layer418 or demand response layer 414 are working properly (e.g., using dataaggregated by AM&V layer 412, integrated control layer 418, buildingsubsystem integration layer 420, FDD layer 416, or otherwise). Thecalculations made by AM&V layer 412 can be based on building systemenergy models and/or equipment models for individual BMS devices orsubsystems. For example, AM&V layer 412 may compare a model-predictedoutput with an actual output from building subsystems 428 to determinean accuracy of the model.

Fault detection and diagnostics (FDD) layer 416 can be configured toprovide on-going fault detection for building subsystems 428, buildingsubsystem devices (i.e., building equipment), and control algorithmsused by demand response layer 414 and integrated control layer 418. FDDlayer 416 may receive data inputs from integrated control layer 418,directly from one or more building subsystems or devices, or fromanother data source. FDD layer 416 may automatically diagnose andrespond to detected faults. The responses to detected or diagnosedfaults can include providing an alert message to a user, a maintenancescheduling system, or a control algorithm configured to attempt torepair the fault or to work-around the fault.

FDD layer 416 can be configured to output a specific identification ofthe faulty component or cause of the fault (e.g., loose damper linkage)using detailed subsystem inputs available at building subsystemintegration layer 420. In other exemplary embodiments, FDD layer 416 isconfigured to provide “fault” events to integrated control layer 418which executes control strategies and policies in response to thereceived fault events. According to some embodiments, FDD layer 416 (ora policy executed by an integrated control engine or business rulesengine) may shut-down systems or direct control activities around faultydevices or systems to reduce energy waste, extend equipment life, orassure proper control response.

FDD layer 416 can be configured to store or access a variety ofdifferent system data stores (or data points for live data). FDD layer416 may use some content of the data stores to identify faults at theequipment level (e.g., specific chiller, specific AHU, specific terminalunit, etc.) and other content to identify faults at component orsubsystem levels. For example, building subsystems 428 may generatetemporal (i.e., time-series) data indicating the performance of BMS 400and the various components thereof. The data generated by buildingsubsystems 428 can include measured or calculated values that exhibitstatistical characteristics and provide information about how thecorresponding system or process (e.g., a temperature control process, aflow control process, etc.) is performing in terms of error from itssetpoint. These processes can be examined by FDD layer 416 to exposewhen the system begins to degrade in performance and alert a user torepair the fault before it becomes more severe.

Referring now to FIG. 5 , a block diagram of another building managementsystem (BMS) 500 is shown, according to some embodiments. BMS 500 can beused to monitor and control the devices of HVAC system 100, watersidesystem 200, airside system 300, building subsystems 428, as well asother types of BMS devices (e.g., lighting equipment, securityequipment, etc.) and/or HVAC equipment.

BMS 500 provides a system architecture that facilitates automaticequipment discovery and equipment model distribution. Equipmentdiscovery can occur on multiple levels of BMS 500 across multipledifferent communications busses (e.g., a system bus 554, zone buses556-560 and 564, sensor/actuator bus 566, etc.) and across multipledifferent communications protocols. In some embodiments, equipmentdiscovery is accomplished using active node tables, which provide statusinformation for devices connected to each communications bus. Forexample, each communications bus can be monitored for new devices bymonitoring the corresponding active node table for new nodes. When a newdevice is detected, BMS 500 can begin interacting with the new device(e.g., sending control signals, using data from the device) without userinteraction.

Some devices in BMS 500 present themselves to the network usingequipment models. An equipment model defines equipment objectattributes, view definitions, schedules, trends, and the associatedBACnet value objects (e.g., analog value, binary value, multistatevalue, etc.) that are used for integration with other systems. Somedevices in BMS 500 store their own equipment models. Other devices inBMS 500 have equipment models stored externally (e.g., within otherdevices). For example, a zone coordinator 508 can store the equipmentmodel for a bypass damper 528. In some embodiments, zone coordinator 508automatically creates the equipment model for bypass damper 528 or otherdevices on zone bus 558. Other zone coordinators can also createequipment models for devices connected to their zone busses. Theequipment model for a device can be created automatically based on thetypes of data points exposed by the device on the zone bus, device type,and/or other device attributes. Several examples of automatic equipmentdiscovery and equipment model distribution are discussed in greaterdetail below.

Still referring to FIG. 5 , BMS 500 is shown to include a system manager502; several zone coordinators 506, 508, 510 and 518; and several zonecontrollers 524, 530, 532, 536, 548, and 550. System manager 502 canmonitor data points in BMS 500 and report monitored variables to variousmonitoring and/or control applications. System manager 502 cancommunicate with client devices 504 (e.g., user devices, desktopcomputers, laptop computers, mobile devices, etc.) via a datacommunications link 574 (e.g., BACnet IP, Ethernet, wired or wirelesscommunications, etc.). System manager 502 can provide a user interfaceto client devices 504 via data communications link 574. The userinterface may allow users to monitor and/or control BMS 500 via clientdevices 504.

In some embodiments, system manager 502 is connected with zonecoordinators 506-510 and 518 via a system bus 554. System manager 502can be configured to communicate with zone coordinators 506-510 and 518via system bus 554 using a master-slave token passing (MSTP) protocol orany other communications protocol. System bus 554 can also connectsystem manager 502 with other devices such as a constant volume (CV)rooftop unit (RTU) 512, an input/output module (TOM) 514, a thermostatcontroller 516 (e.g., a TEC5000 series thermostat controller), and anetwork automation engine (NAE) or third-party controller 520. RTU 512can be configured to communicate directly with system manager 502 andcan be connected directly to system bus 554. Other RTUs can communicatewith system manager 502 via an intermediate device. For example, a wiredinput 562 can connect a third-party RTU 542 to thermostat controller516, which connects to system bus 554.

System manager 502 can provide a user interface for any devicecontaining an equipment model. Devices such as zone coordinators 506-510and 518 and thermostat controller 516 can provide their equipment modelsto system manager 502 via system bus 554. In some embodiments, systemmanager 502 automatically creates equipment models for connected devicesthat do not contain an equipment model (e.g., IOM 514, third partycontroller 520, etc.). For example, system manager 502 can create anequipment model for any device that responds to a device tree request.The equipment models created by system manager 502 can be stored withinsystem manager 502. System manager 502 can then provide a user interfacefor devices that do not contain their own equipment models using theequipment models created by system manager 502. In some embodiments,system manager 502 stores a view definition for each type of equipmentconnected via system bus 554 and uses the stored view definition togenerate a user interface for the equipment.

Each zone coordinator 506-510 and 518 can be connected with one or moreof zone controllers 524, 530-532, 536, and 548-550 via zone buses 556,558, 560, and 564. Zone coordinators 506-510 and 518 can communicatewith zone controllers 524, 530-532, 536, and 548-550 via zone busses556-560 and 564 using a MSTP protocol or any other communicationsprotocol. Zone busses 556-560 and 564 can also connect zone coordinators506-510 and 518 with other types of devices such as variable air volume(VAV) RTUs 522 and 540, changeover bypass (COBP) RTUs 526 and 552,bypass dampers 528 and 546, and PEAK controllers 534 and 544.

Zone coordinators 506-510 and 518 can be configured to monitor andcommand various zoning systems. In some embodiments, each zonecoordinator 506-510 and 518 monitors and commands a separate zoningsystem and is connected to the zoning system via a separate zone bus.For example, zone coordinator 506 can be connected to VAV RTU 522 andzone controller 524 via zone bus 556. Zone coordinator 508 can beconnected to COBP RTU 526, bypass damper 528, COBP zone controller 530,and VAV zone controller 532 via zone bus 558. Zone coordinator 510 canbe connected to PEAK controller 534 and VAV zone controller 536 via zonebus 560. Zone coordinator 518 can be connected to PEAK controller 544,bypass damper 546, COBP zone controller 548, and VAV zone controller 550via zone bus 564.

A single model of zone coordinator 506-510 and 518 can be configured tohandle multiple different types of zoning systems (e.g., a VAV zoningsystem, a COBP zoning system, etc.). Each zoning system can include aRTU, one or more zone controllers, and/or a bypass damper. For example,zone coordinators 506 and 510 are shown as Verasys VAV engines (VVEs)connected to VAV RTUs 522 and 540, respectively. Zone coordinator 506 isconnected directly to VAV RTU 522 via zone bus 556, whereas zonecoordinator 510 is connected to a third-party VAV RTU 540 via a wiredinput 568 provided to PEAK controller 534. Zone coordinators 508 and 518are shown as Verasys COBP engines (VCEs) connected to COBP RTUs 526 and552, respectively. Zone coordinator 508 is connected directly to COBPRTU 526 via zone bus 558, whereas zone coordinator 518 is connected to athird-party COBP RTU 552 via a wired input 570 provided to PEAKcontroller 544.

Zone controllers 524, 530-532, 536, and 548-550 can communicate withindividual BMS devices (e.g., sensors, actuators, etc.) viasensor/actuator (SA) busses. For example, VAV zone controller 536 isshown connected to networked sensors 538 via SA bus 566. Zone controller536 can communicate with networked sensors 538 using a MSTP protocol orany other communications protocol. Although only one SA bus 566 is shownin FIG. 5 , it should be understood that each zone controller 524,530-532, 536, and 548-550 can be connected to a different SA bus. EachSA bus can connect a zone controller with various sensors (e.g.,temperature sensors, humidity sensors, pressure sensors, light sensors,occupancy sensors, etc.), actuators (e.g., damper actuators, valveactuators, etc.) and/or other types of controllable equipment (e.g.,chillers, heaters, fans, pumps, etc.).

Each zone controller 524, 530-532, 536, and 548-550 can be configured tomonitor and control a different building zone. Zone controllers 524,530-532, 536, and 548-550 can use the inputs and outputs provided viatheir SA busses to monitor and control various building zones. Forexample, a zone controller 536 can use a temperature input received fromnetworked sensors 538 via SA bus 566 (e.g., a measured temperature of abuilding zone) as feedback in a temperature control algorithm. Zonecontrollers 524, 530-532, 536, and 548-550 can use various types ofcontrol algorithms (e.g., state-based algorithms, extremum seekingcontrol (ESC) algorithms, proportional-integral (PI) control algorithms,proportional-integral-derivative (PID) control algorithms, modelpredictive control (MPC) algorithms, feedback control algorithms, etc.)to control a variable state or condition (e.g., temperature, humidity,airflow, lighting, etc.) in or around building 10.

Model Predictive Maintenance System

Referring now to FIG. 6 , a block diagram of a building system 600 isshown, according to an exemplary embodiment. System 600 may include manyof the same components as BMS 400 and BMS 500 as described withreference to FIGS. 4-5 . For example, system 600 is shown to includebuilding 10, network 446, and client devices 448. Building 10 is shownto include connected equipment 610, which can include any type ofequipment used to monitor and/or control building 10. Connectedequipment 610 can include connected chillers 612, connected AHUs 614,connected boilers 616, connected batteries 618, or any other type ofequipment in a building system (e.g., heaters, economizers, valves,actuators, dampers, cooling towers, fans, pumps, etc.) or buildingmanagement system (e.g., lighting equipment, security equipment,refrigeration equipment, etc.). Connected equipment 610 can include anyof the equipment of HVAC system 100, waterside system 200, airsidesystem 300, BMS 400, and/or BMS 500, as described with reference toFIGS. 1-5 .

Connected equipment 610 can be outfitted with sensors to monitor variousconditions of the connected equipment 610 (e.g., power consumption,on/off states, operating efficiency, etc.). For example, chillers 612can include sensors configured to monitor chiller variables such aschilled water temperature, condensing water temperature, and refrigerantproperties (e.g., refrigerant pressure, refrigerant temperature, etc.)at various locations in the refrigeration circuit. An example of achiller 700 which can be used as one of chillers 612 is shown in FIG. 7. Chiller 700 is shown to include a refrigeration circuit having acondenser 702, an expansion valve 704, an evaporator 706, a compressor708, and a control panel 710. In some embodiments, chiller 700 includessensors that measure a set of monitored variables at various locationsalong the refrigeration circuit. Similarly, AHUs 614 can be outfittedwith sensors to monitor AHU variables such as supply air temperature andhumidity, outside air temperature and humidity, return air temperatureand humidity, chilled fluid temperature, heated fluid temperature,damper position, etc. In general, connected equipment 610 can monitorand report variables that characterize the performance of the connectedequipment 610. Each monitored variable can be forwarded to buildingmanagement system 606 as a data point including a point ID and a pointvalue.

Monitored variables can include any measured or calculated valuesindicating the performance of connected equipment 610 and/or thecomponents thereof. For example, monitored variables can include one ormore measured or calculated temperatures (e.g., refrigeranttemperatures, cold water supply temperatures, hot water supplytemperatures, supply air temperatures, zone temperatures, etc.),pressures (e.g., evaporator pressure, condenser pressure, supply airpressure, etc.), flow rates (e.g., cold water flow rates, hot water flowrates, refrigerant flow rates, supply air flow rates, etc.), valvepositions, resource consumptions (e.g., power consumption, waterconsumption, electricity consumption, etc.), control setpoints, modelparameters (e.g., regression model coefficients), or any othertime-series values that provide information about how the correspondingsystem, device, or process is performing. Monitored variables can bereceived from connected equipment 610 and/or from various componentsthereof. For example, monitored variables can be received from one ormore controllers (e.g., BMS controllers, subsystem controllers, HVACcontrollers, subplant controllers, AHU controllers, device controllers,etc.), BMS devices (e.g., chillers, cooling towers, pumps, heatingelements, etc.), or collections of BMS devices.

Connected equipment 610 can also report equipment status information.Equipment status information can include, for example, the operationalstatus of the equipment, an operating mode (e.g., low load, medium load,high load, etc.), an indication of whether the equipment is runningunder normal or abnormal conditions, the hours during which theequipment is running, a safety fault code, or any other information thatindicates the current status of connected equipment 610. In someembodiments, each device of connected equipment 610 includes a controlpanel (e.g., control panel 710 shown in FIG. 7 ). Control panel 710 canbe configured to collect monitored variables and equipment statusinformation from connected equipment 610 and provide the collected datato BMS 606. For example, control panel 710 can compare the sensor data(or a value derived from the sensor data) to predetermined thresholds.If the sensor data or calculated value crosses a safety threshold,control panel 710 can shut down the device. Control panel 710 cangenerate a data point when a safety shut down occurs. The data point caninclude a safety fault code which indicates the reason or condition thattriggered the shutdown.

Connected equipment 610 can provide monitored variables and equipmentstatus information to BMS 606. BMS 606 can include a building controller(e.g., BMS controller 366), a system manager (e.g., system manager 503),a network automation engine (e.g., NAE 520), or any other system ordevice of building 10 configured to communicate with connected equipment610. BMS 606 may include some or all of the components of BMS 400 or BMS500, as described with reference to FIGS. 4-5 . In some embodiments, themonitored variables and the equipment status information are provided toBMS 606 as data points. Each data point can include a point ID and apoint value. The point ID can identify the type of data point or avariable measured by the data point (e.g., condenser pressure,refrigerant temperature, power consumption, etc.). Monitored variablescan be identified by name or by an alphanumeric code (e.g.,Chilled_Water_Temp, 7694, etc.). The point value can include analphanumeric value indicating the current value of the data point.

BMS 606 can broadcast the monitored variables and the equipment statusinformation to a model predictive maintenance system 602. In someembodiments, model predictive maintenance system 602 is a component ofBMS 606. For example, model predictive maintenance system 602 can beimplemented as part of a METASYS® brand building automation system, assold by Johnson Controls Inc. In other embodiments, model predictivemaintenance system 602 can be a component of a remote computing systemor cloud-based computing system configured to receive and process datafrom one or more building management systems via network 446. Forexample, model predictive maintenance system 602 can be implemented aspart of a PANOPTIX® brand building efficiency platform, as sold byJohnson Controls Inc. In other embodiments, model predictive maintenancesystem 602 can be a component of a subsystem level controller (e.g., aHVAC controller), a subplant controller, a device controller (e.g., AHUcontroller 330, a chiller controller, etc.), a field controller, acomputer workstation, a client device, or any other system or devicethat receives and processes monitored variables from connected equipment610.

Model predictive maintenance (MPM) system 602 may use the monitoredvariables and/or the equipment status information to identify a currentoperating state of connected equipment 610. The current operating statecan be examined by MPM system 602 to expose when connected equipment 610begins to degrade in performance and/or to predict when faults willoccur. In some embodiments, MPM system 602 uses the informationcollected from connected equipment 610 to estimate the reliability ofconnected equipment 610. For example, MPM system 602 can estimate alikelihood of various types of failures that could potentially occurbased on the current operating conditions of connected equipment 610 andan amount of time that has elapsed since connected equipment 610 hasbeen installed and/or since maintenance was last performed. In someembodiments, MPM system 602 estimates an amount of time until eachfailure is predicted to occur and identifies a financial cost associatedwith each failure (e.g., maintenance cost, increased operating cost,replacement cost, etc.). MPM system 602 can use the reliabilityinformation and the likelihood of potential failures to predict whenmaintenance will be needed and to estimate the cost of performing suchmaintenance over a predetermined time period.

MPM system 602 can be configured to determine an optimal maintenancestrategy for connected equipment 610. In some embodiments, the optimalmaintenance strategy is a set of decisions which optimizes the totalcost associated with purchasing, maintaining, and operating connectedequipment 610 over the duration of an optimization period (e.g., 30weeks, 52 weeks, 10 years, 30 years, etc.). The decisions can include,for example, equipment purchase decisions, equipment maintenancedecisions, and equipment operating decisions. MPM system 602 can use amodel predictive control technique to formulate an objective functionwhich expresses the total cost as a function of these decisions, whichcan be included as decision variables in the objective function. MPMsystem 602 can optimize (i.e., minimize) the objective function usingany of a variety of optimization techniques to identify the optimalvalues for each of the decision variables.

One example of an objective function which can be optimized by MPMsystem 602 is shown in the following equation:

$J = {{\sum\limits_{i = 1}^{h}{C_{{op},i}P_{{op},i}{\Delta t}}} + {\sum\limits_{i = 1}^{h}{C_{{main},i}B_{{main},i}}} + {\sum\limits_{i = 1}^{h}{C_{{cap},i}B_{{cap},i}}}}$where C_(op,i) is the cost per unit of energy (e.g., $/kWh) consumed byconnected equipment 610 at time step i of the optimization period,P_(op,i) is the power consumption (e.g., kW) of connected equipment 610at time step i, Δt is the duration of each time step i, is the cost ofmaintenance performed on connected equipment 610 at time step i,B_(main,i) is a binary variable that indicates whether the maintenanceis performed, C_(cap,i) is the capital cost of purchasing a new deviceof connected equipment 610 at time step i, B_(cap,i) is a binaryvariable that indicates whether the new device is purchased, and h isthe duration of the horizon or optimization period over which theoptimization is performed.

The first term in the objective function J represents the operating costof connected equipment 610 over the duration of the optimization period.In some embodiments, the cost per unit of energy C_(op,i) is receivedfrom a utility 608 as energy pricing data. The cost C_(op,i) may be atime-varying cost that depends on the time of day, the day of the week(e.g., weekday vs. weekend), the current season (e.g., summer vs.winter), or other time-based factors. For example, the cost C_(op,i) maybe higher during peak energy consumption periods and lower duringoff-peak or partial-peak energy consumption periods.

In some embodiments, the power consumption P_(op,i) is based on theheating or cooling load of building 10. The heating or cooling load canbe predicted by MPM system 602 as a function of building occupancy, thetime of day, the day of the week, the current season, or other factorsthat can affect the heating or cooling load. In some embodiments, MPMsystem 602 uses weather forecasts from a weather service 604 to predictthe heating or cooling load. The power consumption P_(op,i) may alsodepend on the efficiency η_(i) of connected equipment 610. For example,connected equipment 610 that operate at a high efficiency may consumeless power P_(op,i) to satisfy the same heating or cooling load relativeto connected equipment 610 that operate at a low efficiency. In general,the power consumption P_(op,i) of a particular device of connectedequipment 610 can be modeled using the following equations:

${P_{{op},i} = \frac{P_{{ideal},i}}{\eta_{i}}}{P_{{ideal},i} = {f\left( {Load}_{i} \right)}}$where Load_(i) is the heating or cooling load on the device at time stepi (e.g., tons cooling, kW heating, etc.), P_(ideal,i) is the value ofthe equipment performance curve (e.g., tons cooling, kW heating, etc.)for the device at the corresponding load point Load_(i), and η_(i) isthe operating efficiency of the device at time step i (e.g., 0≤η_(i)≤1).The function ƒ(Load_(i)) may be defined by the equipment performancecurve for the device or set of devices represented by the performancecurve.

In some embodiments, the equipment performance curve is based onmanufacturer specifications for the device under ideal operatingconditions. For example, the equipment performance curve may define therelationship between power consumption and heating/cooling load for eachdevice of connected equipment 610. However, the actual performance ofthe device may vary as a function of the actual operating conditions.MPM system 602 can analyze the equipment performance informationprovided by connected equipment 610 to determine the operatingefficiency η_(i) for each device of connected equipment 610. In someembodiments, MPM system 602 uses the equipment performance informationfrom connected equipment 610 to determine the actual operatingefficiency η_(i) for each device of connected equipment 610. MPM system602 can use the operating efficiency η_(i) as an input to the objectivefunction/and/or to calculate the corresponding value of P_(op,i).

Advantageously, MPM system 602 can model the efficiency η_(i) ofconnected equipment 610 at each time step i as a function of themaintenance decisions and the equipment purchase decisions B_(cap,i).For example, the efficiency η_(i) for a particular device may start atan initial value η₀ when the device is purchased and may degrade overtime such that the efficiency η_(i) decreases with each successive timestep i. Performing maintenance on a device may reset the efficiencyη_(i) to a higher value immediately after the maintenance is performed.Similarly, purchasing a new device to replace an existing device mayreset the efficiency η_(i) to a higher value immediately after the newdevice is purchased. After being reset, the efficiency η_(i) maycontinue to degrade over time until the next time at which maintenanceis performed or a new device is purchased.

Performing maintenance or purchasing a new device may result in arelatively lower power consumption P_(op,i) during operation andtherefore a lower operating cost at each time step i after themaintenance is performed or the new device is purchased. In other words,performing maintenance or purchasing a new device may decrease theoperating cost represented by the first term of the objective functionJ. However, performing maintenance may increase the second term of theobjective function J and purchasing a new device may increase the thirdterm of the objective function J. The objective function J captures eachof these costs and can be optimized by MPM system 602 to determine theoptimal set of maintenance and equipment purchase decisions (i.e.,optimal values for the binary decision variables B_(main,i) andB_(cap,i)) over the duration of the optimization period.

In some embodiments, MPM system 602 uses the equipment performanceinformation from connected equipment 610 to estimate the reliability ofconnected equipment 610. The reliability may be a statistical measure ofthe likelihood that connected equipment 610 will continue operatingwithout fault under its current operating conditions. Operating undermore strenuous conditions (e.g., high load, high temperatures, etc.) mayresult in a lower reliability, whereas operating under less strenuousconditions (e.g., low load, moderate temperatures, etc.) may result in ahigher reliability. In some embodiments, the reliability is based on anamount of time that has elapsed since connected equipment 610 lastreceived maintenance.

MPM system 602 may receive operating data from a plurality of devices ofconnected equipment 610 distributed across multiple buildings and canuse the set of operating data (e.g., operating conditions, faultindications, failure times, etc.) to develop a reliability model foreach type of equipment. The reliability models can be used by MPM system602 to estimate the reliability of any given device of connectedequipment 610 as a function of its current operating conditions and/orother extraneous factors (e.g., time since maintenance was lastperformed, geographic location, water quality, etc.). In someembodiments, MPM system 602 uses the estimated reliability of eachdevice of connected equipment 610 to determine the probability that thedevice will require maintenance and/or replacement at each time step ofthe optimization period. MPM system 602 can use these probabilities todetermine the optimal set of maintenance and equipment purchasedecisions (i.e., optimal values for the binary decision variablesB_(main,i) and B_(cap,i)) over the duration of the optimization period.

In some embodiments, MPM system 602 generates and provides equipmentpurchase and maintenance recommendations. The equipment purchase andmaintenance recommendations may be based on the optimal values for thebinary decision variables B_(main,i) and B_(cap,i) determined byoptimizing the objective function J. For example, a value ofB_(main,25)=1 for a particular device of connected equipment 610 mayindicate that maintenance should be performed on that device at the25^(th) time step of the optimization period, whereas a value ofB_(main,25)=0 may indicate that the maintenance should not be performedat that time step. Similarly, a value of B_(cap,25)=1 may indicate thata new device of connected equipment 610 should be purchased at the25^(th) time step of the optimization period, whereas a value ofB_(cap,25)=0 may indicate that the new device should not be purchased atthat time step.

Advantageously, the equipment purchase and maintenance recommendationsgenerated by MPM system 602 are predictive recommendations based on theactual operating conditions and actual performance of connectedequipment 610. The optimization performed by MPM system 602 weighs thecost of performing maintenance and the cost of purchasing new equipmentagainst the decrease in operating cost resulting from such maintenanceor purchase decisions in order to determine the optimal maintenancestrategy that minimizes the total combined cost J. In this way, theequipment purchase and maintenance recommendations generated by MPMsystem 602 may be specific to each group of connected equipment 610 inorder to achieve the optimal cost J for that specific group of connectedequipment 610. The equipment-specific recommendations may result in alower overall cost J relative to generic preventative maintenancerecommendations provided by an equipment manufacturer (e.g., serviceequipment every year) which may be sub-optimal for some groups ofconnected equipment 610 and/or some operating conditions.

In some embodiments, the equipment purchase and maintenancerecommendations are provided to building 10 (e.g., to BMS 606) and/or toclient devices 448. An operator or building owner can use the equipmentpurchase and maintenance recommendations to assess the costs andbenefits of performing maintenance and purchasing new devices. In someembodiments, the equipment purchase and maintenance recommendations areprovided to service technicians 620. Service technicians 620 can use theequipment purchase and maintenance recommendations to determine whencustomers should be contacted to perform service or replace equipment.

In some embodiments, MPM system 602 includes a data analytics andvisualization platform. MPM system 602 may provide a web interface whichcan be accessed by service technicians 620, client devices 448, andother systems or devices. The web interface can be used to access theequipment performance information, view the results of the optimization,identify which equipment is in need of maintenance, and otherwiseinteract with MPM system 602. Service technicians 620 can access the webinterface to view a list of equipment for which maintenance isrecommended by MPM system 602. Service technicians 620 can use theequipment purchase and maintenance recommendations to proactively repairor replace connected equipment 610 in order to achieve the optimal costpredicted by the objective function J. These and other features of MPMsystem 602 are described in greater detail below.

Referring now to FIG. 8 , a block diagram illustrating MPM system 602 ingreater detail is shown, according to an exemplary embodiment. MPMsystem 602 is shown providing optimization results to a buildingmanagement system (BMS) 606. BMS 606 can include some or all of thefeatures of BMS 400 and/or BMS 500, as described with reference to FIGS.4-5 . The optimization results provided to BMS 606 may include theoptimal values of the decision variables in the objective function J foreach time step i in the optimization period. In some embodiments, theoptimization results include equipment purchase and maintenancerecommendations for each device of connected equipment 610.

BMS 606 may be configured to monitor the operation and performance ofconnected equipment 610. BMS 606 may receive monitored variables fromconnected equipment 610. Monitored variables can include any measured orcalculated values indicating the performance of connected equipment 610and/or the components thereof. For example, monitored variables caninclude one or more measured or calculated temperatures, pressures, flowrates, valve positions, resource consumptions (e.g., power consumption,water consumption, electricity consumption, etc.), control setpoints,model parameters (e.g., equipment model coefficients), or any othervariables that provide information about how the corresponding system,device, or process is performing.

In some embodiments, the monitored variables indicate the operatingefficiency η_(i) of each device of connected equipment 610 or can beused to calculate the operating efficiency η_(i). For example, thetemperature and flow rate of chilled water output by a chiller can beused to calculate the cooling load (e.g., tons cooling) served by thechiller. The cooling load can be used in combination with the powerconsumption of the chiller to calculate the operating efficiency η_(i)(e.g., tons cooling per kW of electricity consumed). BMS 606 may reportthe monitored variables to MPM system 602 for use in calculating theoperating efficiency η_(i) of each device of connected equipment 610.

In some embodiments, BMS 606 monitors the run hours of connectedequipment 610. The run hours may indicate the number of hours within agiven time period during which each device of connected equipment 610 isactive. For example, the run hours for a chiller may indicate that thechiller is active for approximately eight hours per day. The run hourscan be used in combination with the average power consumption of thechiller when active to estimate the total power consumption P_(op,i) ofconnected equipment 610 at each time step i.

In some embodiments, BMS 606 monitors the equipment failures and faultindications reported by connected equipment 610. BMS 606 can record thetimes at which each failure or fault occurs and the operating conditionsof connected equipment 610 under which the fault or failure occurred.The operating data collected from connected equipment 610 can be used byBMS 606 and/or MPM system 602 to develop a reliability model for eachdevice of connected equipment 610. BMS 606 may provide the monitoredvariables, the equipment run hours, the operating conditions, and theequipment failures and fault indications to MPM system 602 as equipmentperformance information.

BMS 606 may be configured to monitor conditions within a controlledbuilding or building zone. For example, BMS 606 may receive input fromvarious sensors (e.g., temperature sensors, humidity sensors, airflowsensors, voltage sensors, etc.) distributed throughout the building andmay report building conditions to MPM system 602. Building conditionsmay include, for example, a temperature of the building or a zone of thebuilding, a power consumption (e.g., electric load) of the building, astate of one or more actuators configured to affect a controlled statewithin the building, or other types of information relating to thecontrolled building. BMS 606 may operate connected equipment 610 toaffect the monitored conditions within the building and to serve thethermal energy loads of the building.

BMS 606 may provide control signals to connected equipment 610specifying on/off states, charge/discharge rates, and/or setpoints forconnected equipment 610. BMS 606 may control the equipment (e.g., viaactuators, power relays, etc.) in accordance with the control signals toachieve setpoints for various building zones and/or devices of connectedequipment 610. In various embodiments, BMS 606 may be combined with MPMsystem 602 or may be part of a separate building management system.According to an exemplary embodiment, BMS 606 is a METASYS® brandbuilding management system, as sold by Johnson Controls, Inc.

MPM system 602 may monitor the performance of connected equipment 610using information received from BMS 606. MPM system 602 may beconfigured to predict the thermal energy loads (e.g., heating loads,cooling loads, etc.) of the building for plurality of time steps in theoptimization period (e.g., using weather forecasts from a weatherservice 604). MPM system 602 may also predict the cost of electricity orother resources (e.g., water, natural gas, etc.) using pricing datareceived from utilities 608. MPM system 602 may generate optimizationresults that optimize the economic value of operating, maintaining, andpurchasing connected equipment 610 over the duration of the optimizationperiod subject to constraints on the optimization process (e.g., loadconstraints, decision variable constraints, etc.). The optimizationprocess performed by MPM system 602 is described in greater detailbelow.

According to an exemplary embodiment, MPM system 602 can be integratedwithin a single computer (e.g., one server, one housing, etc.). Invarious other exemplary embodiments, MPM system 602 can be distributedacross multiple servers or computers (e.g., that can exist indistributed locations). In another exemplary embodiment, MPM system 602may integrated with a smart building manager that manages multiplebuilding systems and/or combined with BMS 606.

MPM system 602 is shown to include a communications interface 804 and aprocessing circuit 806. Communications interface 804 may include wiredor wireless interfaces (e.g., jacks, antennas, transmitters, receivers,transceivers, wire terminals, etc.) for conducting data communicationswith various systems, devices, or networks. For example, communicationsinterface 804 may include an Ethernet card and port for sending andreceiving data via an Ethernet-based communications network and/or aWiFi transceiver for communicating via a wireless communicationsnetwork. Communications interface 804 may be configured to communicatevia local area networks or wide area networks (e.g., the Internet, abuilding WAN, etc.) and may use a variety of communications protocols(e.g., BACnet, IP, LON, etc.).

Communications interface 804 may be a network interface configured tofacilitate electronic data communications between MPM system 602 andvarious external systems or devices (e.g., BMS 606, connected equipment610, utilities 510, etc.). For example, MPM system 602 may receiveinformation from BMS 606 indicating one or more measured states of thecontrolled building (e.g., temperature, humidity, electric loads, etc.)and equipment performance information for connected equipment 610 (e.g.,run hours, power consumption, operating efficiency, etc.).Communications interface 804 may receive inputs from BMS 606 and/orconnected equipment 610 and may provide optimization results to BMS 606and/or other external systems or devices. The optimization results maycause BMS 606 to activate, deactivate, or adjust a setpoint forconnected equipment 610 in order to achieve the optimal values of thedecision variables specified in the optimization results.

Still referring to FIG. 8 , processing circuit 806 is shown to include aprocessor 808 and memory 810. Processor 808 may be a general purpose orspecific purpose processor, an application specific integrated circuit(ASIC), one or more field programmable gate arrays (FPGAs), a group ofprocessing components, or other suitable processing components.Processor 808 may be configured to execute computer code or instructionsstored in memory 810 or received from other computer readable media(e.g., CDROM, network storage, a remote server, etc.).

Memory 810 may include one or more devices (e.g., memory units, memorydevices, storage devices, etc.) for storing data and/or computer codefor completing and/or facilitating the various processes described inthe present disclosure. Memory 810 may include random access memory(RAM), read-only memory (ROM), hard drive storage, temporary storage,non-volatile memory, flash memory, optical memory, or any other suitablememory for storing software objects and/or computer instructions. Memory810 may include database components, object code components, scriptcomponents, or any other type of information structure for supportingthe various activities and information structures described in thepresent disclosure. Memory 810 may be communicably connected toprocessor 808 via processing circuit 806 and may include computer codefor executing (e.g., by processor 808) one or more processes describedherein.

MPM system 602 is shown to include an equipment performance monitor 824.Equipment performance monitor 824 can receive equipment performanceinformation from BMS 606 and/or connected equipment 610. The equipmentperformance information can include samples of monitored variables(e.g., measured temperature, measured pressure, measured flow rate,power consumption, etc.), current operating conditions (e.g., heating orcooling load, current operating state, etc.), fault indications, orother types of information that characterize the performance ofconnected equipment 610. In some embodiments, equipment performancemonitor 824 uses the equipment performance information to calculate thecurrent efficiency and reliability of each device of connected equipment610. Equipment performance monitor 824 can provide the efficiency η_(i)and reliability values to model predictive optimizer 830 for use inoptimizing the objective function J.

Still referring to FIG. 8 , MPM system 602 is shown to include aload/rate predictor 822. Load/rate predictor 822 may be configured topredict the energy loads (Load_(i)) (e.g., heating load, cooling load,electric load, etc.) of the building or campus for each time step i ofthe optimization period. Load/rate predictor 822 is shown receivingweather forecasts from a weather service 604. In some embodiments,load/rate predictor 822 predicts the energy loads Load_(i) as a functionof the weather forecasts. In some embodiments, load/rate predictor 822uses feedback from BMS 606 to predict loads Load_(i). Feedback from BMS606 may include various types of sensory inputs (e.g., temperature,flow, humidity, enthalpy, etc.) or other data relating to the controlledbuilding (e.g., inputs from a HVAC system, a lighting control system, asecurity system, a water system, etc.).

In some embodiments, load/rate predictor 822 receives a measuredelectric load and/or previous measured load data from BMS 606 (e.g., viaequipment performance monitor 824). Load/rate predictor 822 may predictloads Load_(i) as a function of a given weather forecast ({circumflexover (ϕ)}_(w)), a day type (day), the time of day (t), and previousmeasured load data (Y_(i-1)). Such a relationship is expressed in thefollowing equation:Load_(i)=ƒ({circumflex over (ϕ)}_(w),day,t|Y _(i-1))

In some embodiments, load/rate predictor 822 uses a deterministic plusstochastic model trained from historical load data to predict loadsLoad_(i). Load/rate predictor 822 may use any of a variety of predictionmethods to predict loads Load_(i) (e.g., linear regression for thedeterministic portion and an AR model for the stochastic portion).Load/rate predictor 822 may predict one or more different types of loadsfor the building or campus. For example, load/rate predictor 822 maypredict a hot water load Load_(Hot,i), a cold water load Load_(Cold,i),and an electric load Load_(Elec,i) for each time step i within theoptimization period. The predicted load values Load_(i) can include someor all of these types of loads. In some embodiments, load/rate predictor822 makes load/rate predictions using the techniques described in U.S.patent application Ser. No. 14/717,593 filed May 20, 2015, the entiredisclosure of which is incorporated by reference herein.

Load/rate predictor 822 is shown receiving utility rates from utilities608. Utility rates may indicate a cost or price per unit of a resource(e.g., electricity, natural gas, water, etc.) provided by utilities 608at each time step i in the optimization period. In some embodiments, theutility rates are time-variable rates. For example, the price ofelectricity may be higher at certain times of day or days of the week(e.g., during high demand periods) and lower at other times of day ordays of the week (e.g., during low demand periods). The utility ratesmay define various time periods and a cost per unit of a resource duringeach time period. Utility rates may be actual rates received fromutilities 608 or predicted utility rates estimated by load/ratepredictor 822.

In some embodiments, the utility rates include demand charges for one ormore resources provided by utilities 608. A demand charge may define aseparate cost imposed by utilities 608 based on the maximum usage of aparticular resource (e.g., maximum energy consumption) during a demandcharge period. The utility rates may define various demand chargeperiods and one or more demand charges associated with each demandcharge period. In some instances, demand charge periods may overlappartially or completely with each other and/or with the predictionwindow. Model predictive optimizer 830 may be configured to account fordemand charges in the high level optimization process performed by highlevel optimizer 832. Utilities 608 may be defined by time-variable(e.g., hourly) prices, a maximum service level (e.g., a maximum rate ofconsumption allowed by the physical infrastructure or by contract) and,in the case of electricity, a demand charge or a charge for the peakrate of consumption within a certain period. Load/rate predictor 822 maystore the predicted loads Load_(i) and the utility rates in memory 810and/or provide the predicted loads Load_(i) and the utility rates tomodel predictive optimizer 830.

Still referring to FIG. 8 , MPM system 602 is shown to include a modelpredictive optimizer 830. Model predictive optimizer 830 can beconfigured to perform a multi-level optimization process to optimize thetotal cost associated with purchasing, maintaining, and operatingconnected equipment 610. In some embodiments, model predictive optimizer830 includes a high level optimizer 832 and a low level optimizer 834.High level optimizer 832 may optimize the objective function/for anentire set of connected equipment 610 (e.g., all of the devices within abuilding) or for a subset of connected equipment 610 (e.g., a singledevice, all of the devices of a subplant or building subsystem, etc.) todetermine the optimal values for each of the decision variables (e.g.,P_(op,i), B_(main,i), and B_(cap,i)) in the objective function J. Theoptimization performed by high level optimizer 832 is described ingreater detail with reference to FIG. 9 .

In some embodiments, low level optimizer 834 receives the optimizationresults from high level optimizer 832. The optimization results mayinclude optimal power consumption values P_(op,i) and/or load valuesLoad_(i) for each device or set of devices of connected equipment ateach time step i in the optimization period. Low level optimizer 834 maydetermine how to best run each device or set of devices at the loadvalues determined by high level optimizer 832. For example, low leveloptimizer 834 may determine on/off states and/or operating setpoints forvarious devices of connected equipment 610 in order to optimize (e.g.,minimize) the power consumption of connected equipment 610 meeting thecorresponding load value Load_(i).

Low level optimizer 834 may be configured to generate equipmentperformance curves for each device or set of devices of connectedequipment 610. Each performance curve may indicate an amount of resourceconsumption (e.g., electricity use measured in kW, water use measured inL/s, etc.) by a particular device or set of devices of connectedequipment 610 as a function of the load on the device or set of devices.In some embodiments, low level optimizer 834 generates the performancecurves by performing a low level optimization process at variouscombinations of load points (e.g., various values of Load_(i)) andweather conditions to generate multiple data points. The low leveloptimization may be used to determine the minimum amount of resourceconsumption required to satisfy the corresponding heating or coolingload. An example of a low level optimization process which can beperformed by low level optimizer 834 is described in detail in U.S.patent application Ser. No. 14/634,615 titled “Low Level Central PlantOptimization” and filed Feb. 27, 2015, the entire disclosure of which isincorporated by reference herein. Low level optimizer 834 may fit acurve to the data points to generate the performance curves.

In some embodiments, low level optimizer 834 generates equipmentperformance curves for a set of connected equipment 610 (e.g., a chillersubplant, a heater subplant, etc.) by combining efficiency curves forindividual devices of connected equipment 610. A device efficiency curvemay indicate the amount of resource consumption by the device as afunction of load. The device efficiency curves may be provided by adevice manufacturer or generated using experimental data. In someembodiments, the device efficiency curves are based on an initialefficiency curve provided by a device manufacturer and updated usingexperimental data. The device efficiency curves may be stored inequipment models 818. For some devices, the device efficiency curves mayindicate that resource consumption is a U-shaped function of load.Accordingly, when multiple device efficiency curves are combined into aperformance curve for multiple devices, the resultant performance curvemay be a wavy curve. The waves are caused by a single device loading upbefore it is more efficient to turn on another device to satisfy thesubplant load. Low level optimizer 834 may provide the equipmentperformance curves to high level optimizer 832 for use in the high leveloptimization process.

Still referring to FIG. 8 , MPM system 602 is shown to include anequipment controller 828. Equipment controller 828 can be configured tocontrol connected equipment 610 to affect a variable state or conditionin building 10 (e.g., temperature, humidity, etc.). In some embodiments,equipment controller 828 controls connected equipment 610 based on theresults of the optimization performed by model predictive optimizer 830.In some embodiments, equipment controller 828 generates control signalswhich can be provided to connected equipment 610 via communicationsinterface 804 and/or BMS 606. The control signals may be based on theoptimal values of the decision variables in the objective function J.For example, equipment controller 828 may generate control signals whichcause connected equipment 610 to achieve the optimal power consumptionvalues P_(op,i) for each time step i in the optimization period.

Data and processing results from model predictive optimizer 830,equipment controller 828, or other modules of MPM system 602 may beaccessed by (or pushed to) monitoring and reporting applications 826.Monitoring and reporting applications 826 may be configured to generatereal time “system health” dashboards that can be viewed and navigated bya user (e.g., a system engineer). For example, monitoring and reportingapplications 826 may include a web-based monitoring application withseveral graphical user interface (GUI) elements (e.g., widgets,dashboard controls, windows, etc.) for displaying key performanceindicators (KPI) or other information to users of a GUI. In addition,the GUI elements may summarize relative energy use and intensity acrossbuilding management systems in different buildings (real or modeled),different campuses, or the like. Other GUI elements or reports may begenerated and shown based on available data that allow users to assessperformance across one or more energy storage systems from one screen.The user interface or report (or underlying data engine) may beconfigured to aggregate and categorize operating conditions by building,building type, equipment type, and the like. The GUI elements mayinclude charts or histograms that allow the user to visually analyze theoperating parameters and power consumption for the devices of thebuilding system.

Still referring to FIG. 8 , MPM system 602 may include one or more GUIservers, web services 812, or GUI engines 814 to support monitoring andreporting applications 826. In various embodiments, applications 826,web services 812, and GUI engine 814 may be provided as separatecomponents outside of MPM system 602 (e.g., as part of a smart buildingmanager). MPM system 602 may be configured to maintain detailedhistorical databases (e.g., relational databases, XML databases, etc.)of relevant data and includes computer code modules that continuously,frequently, or infrequently query, aggregate, transform, search, orotherwise process the data maintained in the detailed databases. MPMsystem 602 may be configured to provide the results of any suchprocessing to other databases, tables, XML files, or other datastructures for further querying, calculation, or access by, for example,external monitoring and reporting applications.

MPM system 602 is shown to include configuration tools 816.Configuration tools 816 can allow a user to define (e.g., via graphicaluser interfaces, via prompt-driven “wizards,” etc.) how MPM system 602should react to changing conditions in BMS 606 and/or connectedequipment 610. In an exemplary embodiment, configuration tools 816 allowa user to build and store condition-response scenarios that can crossmultiple devices of connected equipment 610, multiple building systems,and multiple enterprise control applications (e.g., work ordermanagement system applications, entity resource planning applications,etc.). For example, configuration tools 816 can provide the user withthe ability to combine data (e.g., from subsystems, from eventhistories) using a variety of conditional logic. In varying exemplaryembodiments, the conditional logic can range from simple logicaloperators between conditions (e.g., AND, OR, XOR, etc.) to pseudo-codeconstructs or complex programming language functions (allowing for morecomplex interactions, conditional statements, loops, etc.).Configuration tools 816 can present user interfaces for building suchconditional logic. The user interfaces may allow users to definepolicies and responses graphically. In some embodiments, the userinterfaces may allow a user to select a pre-stored or pre-constructedpolicy and adapt it or enable it for use with their system.

High Level Optimizer

Referring now to FIG. 9 , a block diagram illustrating high leveloptimizer 832 in greater detail is shown, according to an exemplaryembodiment. High level optimizer 832 can be configured to determine anoptimal maintenance strategy for connected equipment 610. In someembodiments, the optimal maintenance strategy is a set of decisionswhich optimizes the total cost associated with purchasing, maintaining,and operating connected equipment 610 over the duration of anoptimization period (e.g., 30 weeks, 52 weeks, 10 years, 30 years,etc.). The decisions can include, for example, equipment purchasedecisions, equipment maintenance decisions, and equipment operatingdecisions.

High level optimizer 832 is shown to include an operational costpredictor 910, a maintenance cost predictor 920, a capital costpredictor 930, an objective function generator 935, and an objectivefunction optimizer 940. Cost predictors 910, 920, and 930 can use amodel predictive control technique to formulate an objective functionwhich expresses the total cost as a function of several decisionvariables (e.g., maintenance decisions, equipment purchase decisions,etc.) and input parameters (e.g., energy cost, device efficiency, devicereliability). Operational cost predictor 910 can be configured toformulate an operational cost term in the objective function. Similarly,maintenance cost predictor 920 can be configured to formulate amaintenance cost term in the objective function and capital costpredictor 930 can be configured to formulate a capital cost term in theobjective function. Objective function optimizer 940 can optimize (i.e.,minimize) the objective function using any of a variety of optimizationtechniques to identify the optimal values for each of the decisionvariables.

One example of an objective function which can be generated by highlevel optimizer 832 is shown in the following equation:

$J = {{\sum\limits_{i = 1}^{h}{C_{{op},i}P_{{op},i}{\Delta t}}} + {\sum\limits_{i = 1}^{h}{C_{{main},i}B_{{main},i}}} + {\sum\limits_{i = 1}^{h}{C_{{cap},i}B_{{cap},i}}}}$where C_(op,i) is the cost per unit of energy (e.g., $/kWh) consumed byconnected equipment 610 at time step i of the optimization period,P_(op,i) is the power consumption (e.g., kW) of connected equipment 610at time step i, Δt is the duration of each time step i, C_(main,i) isthe cost of maintenance performed on connected equipment 610 at timestep i, B_(main,i) is a binary variable that indicates whether themaintenance is performed, C_(cap,i) is the capital cost of purchasing anew device of connected equipment 610 at time step i, B_(cap,i) is abinary variable that indicates whether the new device is purchased, andh is the duration of the horizon or optimization period over which theoptimization is performed.Operational Cost Predictor

Operational cost predictor 910 can be configured to formulate the firstterm in the objective function J. The first term in the objectivefunction J represents the operating cost of connected equipment 610 overthe duration of the optimization period and is shown to include threevariables or parameters (i.e., C_(op,i), P_(op,i), and Δt). In someembodiments, the cost per unit of energy C_(op,i) is determined byenergy costs module 915. Energy costs module 915 can receive a set ofenergy prices from utility 608 as energy pricing data. In someembodiments, the energy prices are time-varying cost that depend on thetime of day, the day of the week (e.g., weekday vs. weekend), thecurrent season (e.g., summer vs. winter), or other time-based factors.For example, the cost of electricity may be higher during peak energyconsumption periods and lower during off-peak or partial-peak energyconsumption periods.

Energy costs module 915 can use the energy costs to define the value ofC_(op,i) for each time step i of the optimization period. In someembodiments, energy costs module 915 stores the energy costs as an arrayC_(op) including a cost element for each of the h time steps in theoptimization period. For example, energy costs module 915 can generatethe following array:C _(op) =[C _(op,1) C _(op,2) . . . C _(op,h)]where the array C_(op) has a size of 1×h and each element of the arrayC_(op) includes an energy cost value C_(op,i) for a particular time stepi=1 . . . h of the optimization period.

Still referring to FIG. 9 , operational cost predictor 910 is shown toinclude an ideal performance calculator 912. Ideal performancecalculator 912 may receive load predictions Load_(i) from load/ratepredictor 822 and may receive performance curves from low leveloptimizer 834. As discussed above, the performance curves may define theideal power consumption P_(ideal) of a device or set of devices ofconnected equipment 610 as a function of the heating or cooling load onthe device or set of devices. For example, the performance curve one ormore devices of connected equipment 610 can be defined by the followingequation:P _(ideal,i)=ƒ(Load_(i))where P_(ideal,i) is the ideal power consumption (e.g., kW) of connectedequipment 610 at time step i and Load_(i) is the load (e.g., tonscooling, kW heating, etc.) on connected equipment 610 at time step i.The ideal power consumption P_(ideal,i) may represent the powerconsumption of the one or more devices of connected equipment 610assuming they operate at perfect efficiency.

Ideal performance calculator 912 can use the performance curve for adevice or set of devices of connected equipment 610 to identify thevalue of P_(ideal,i) that corresponds to the load point Load_(i) for thedevice or set of devices at each time step of the optimization period.In some embodiments, ideal performance calculator 912 stores the idealload values as an array P_(ideal) including an element for each of the htime steps in the optimization period. For example, ideal performancecalculator 912 can generate the following array:P _(ideal) =[P _(ideal,1) P _(ideal,2) . . . P _(ideal,h)]^(T)where the array P_(ideal) has a size of h×1 and each element of thearray P_(ideal) includes an ideal power consumption value P_(ideal,i)for a particular time step i=1 . . . h of the optimization period.

Still referring to FIG. 9 , operational cost predictor 910 is shown toinclude an efficiency updater 911 and an efficiency degrader 913.Efficiency updater 911 can be configured to determine the efficiency ηof connected equipment 610 under actual operating conditions. In someembodiments, the efficiency η_(i) represents the ratio of the idealpower consumption P_(ideal) of connected equipment to the actual powerconsumption P_(actual) of connected equipment 610, as shown in thefollowing equation:

$\eta = \frac{P_{ideal}}{P_{actual}}$where P_(ideal) is the ideal power consumption of connected equipment610 as defined by the performance curve for connected equipment 610 andP_(actual) is the actual power consumption of connected equipment 610.In some embodiments, efficiency updater 911 uses the equipmentperformance information collected from connected equipment 610 toidentify the actual power consumption value P_(actual). Efficiencyupdater 911 can use the actual power consumption P_(actual) incombination with the ideal power consumption P_(ideal) to calculate theefficiency η.

Efficiency updater 911 can be configured to periodically update theefficiency η to reflect the current operating efficiency of connectedequipment 610. For example, efficiency updater 911 can calculate theefficiency η of connected equipment 610 once per day, once per week,once per year, or at any other interval as may be suitable to capturechanges in the efficiency i over time. Each value of the efficiency imay be based on corresponding values of P_(ideal) and P_(actual) at thetime the efficiency η is calculated. In some embodiments, efficiencyupdater 911 updates the efficiency η each time the high leveloptimization process is performed (i.e., each time the objectivefunction J is optimized). The efficiency value calculated by efficiencyupdater 911 may be stored in memory 810 as an initial efficiency valueη₀, where the subscript 0 denotes the value of the efficiency η at orbefore the beginning of the optimization period (e.g., at time step 0).

In some embodiments, efficiency updater 911 updates the efficiency η_(i)for one or more time steps during the optimization period to account forincreases in the efficiency η of connected equipment 610 that willresult from performing maintenance on connected equipment 610 orpurchasing new equipment to replace or supplement one or more devices ofconnected equipment 610. The time steps i at which the efficiency η_(i)is updated may correspond to the predicted time steps at which themaintenance will be performed or the equipment will replaced. Thepredicted time steps at which maintenance will be performed on connectedequipment 610 may be defined by the values of the binary decisionvariables B_(main,i) in the objective function J. Similarly, thepredicted time steps at which the equipment will be replaced may bedefined by the values of the binary decision variables B_(cap,i) in theobjective function J.

Efficiency updater 911 can be configured to reset the efficiency η_(i)for a given time step i if the binary decision variables B_(main,i) andB_(cap,i) indicate that maintenance will be performed at that time stepand/or new equipment will be purchased at that time step (i.e.,B_(main,i)=1 and/or B_(cap,i)=1). For example, if B_(main,i)=1,efficiency updater 911 can be configured to reset the value of η_(i) toη_(main), where η_(main) is the efficiency value that is expected toresult from the maintenance performed at time step i. Similarly, ifB_(cap,i)=1, efficiency updater 911 can be configured to reset the valueof η_(i) to η_(cap), where η_(cap) is the efficiency value that isexpected to result from purchasing a new device to supplement or replaceone or more devices of connected equipment 610 performed at time step i.Efficiency updater 911 can dynamically reset the efficiency η_(i) forone or more time steps while the optimization is being performed (e.g.,with each iteration of the optimization) based on the values of binarydecision variables B_(main,i) and B_(cap,i).

Efficiency degrader 913 can be configured to predict the efficiencyη_(i) of connected equipment 610 at each time step i of the optimizationperiod. The initial efficiency η₀ at the beginning of the optimizationperiod may degrade over time as connected equipment 610 degrade inperformance. For example, the efficiency of a chiller may degrade overtime as a result of the chilled water tubes becoming dirty and reducingthe heat transfer coefficient of the chiller. Similarly, the efficiencyof a battery may decrease over time as a result of degradation in thephysical or chemical components of the battery. Efficiency degrader 913can be configured to account for such degradation by incrementallyreducing the efficiency η_(i) over the duration of the optimizationperiod.

In some embodiments, the initial efficiency value η₀ is updated at thebeginning of each optimization period. However, the efficiency η maydegrade during the optimization period such that the initial efficiencyvalue η₀ becomes increasingly inaccurate over the duration of theoptimization period. To account for efficiency degradation during theoptimization period, efficiency degrader 913 can decrease the efficiencyη by a predetermined amount with each successive time step. For example,efficiency degrader 913 can define the efficiency at each time step i=1. . . h as follows:η_(i)=η_(i-1)−Δηwhere η_(i) is the efficiency at time step i, η_(i-1) is the efficiencyat time step i−1, and Δη is the degradation in efficiency betweenconsecutive time steps. In some embodiments, this definition of η_(i) isapplied to each time step for which B_(main,i)=0 and B_(cap,i)=0.However, if either B_(main,i)=1 or B_(cap,i)=1, the value of η_(i) maybe reset to either η_(main) or η_(cap) as previously described.

In some embodiments, the value of Δη is based on a time series ofefficiency values calculated by efficiency updater 911. For example,efficiency degrader 913 may record a time series of the initialefficiency values η₀ calculated by efficiency updater 911, where each ofthe initial efficiency values η₀ represents the empirically-calculatedefficiency of connected equipment 610 at a particular time. Efficiencydegrader 913 can examine the time series of initial efficiency values η₀to determine the rate at which the efficiency degrades. For example, ifthe initial efficiency η₀ at time t₁ is η_(0,1) and the initialefficiency at time t₂ is η_(0.2), efficiency degrader 913 can calculatethe rate of efficiency degradation as follows:

$\frac{\Delta\eta}{\Delta t} = {\frac{\eta_{0,2} - \eta_{0,1}}{t_{2} - t_{1}}{where}\frac{\Delta\eta}{\Delta t}}$is the rate of efficiency degradation. Efficiency degrader 913 canmultiply

$\frac{\Delta\eta}{\Delta t}$by the duration of each time step Δt to calculate the value of Δη

$\left( {{i.e.},{{\Delta\eta} = {\frac{\Delta\eta}{\Delta t}*{\Delta t}}}} \right).$

In some embodiments, efficiency degrader 913 stores the efficiencyvalues over the duration of the optimization period in an array ηincluding an element for each of the h time steps in the optimizationperiod. For example, efficiency degrader 913 can generate the followingarray:η=[η₁η₂ . . . η_(h)]where the array η has a size of 1×h and each element of the array ηincludes an efficiency value η_(i) for a particular time step i=1 . . .h of the optimization period. Each element i of the array η may becalculated based on the value of the previous element and the value ofΔη (e.g., if B_(main,i)=0 and B_(cap,i)=0) or may be dynamically resetto either η_(main) or η_(cap) (e.g., if B_(main,i)=1 or B_(cap,i)=1.

The logic characterizing the efficiency updating and resettingoperations performed by efficiency updater 911 and efficiency degrader913 can be summarized in the following equations:if B _(main,i)=1→η_(i)=η_(main)if B _(cap,i)=1→η_(i)=η_(cap)if B _(main,i)=0 and B _(cap,i)=0→η_(i)=η_(i-1)−Δηwhich can be applied as constraints on the high level optimizationperformed by objective function optimizer 940.

Advantageously, efficiency updater 911 and efficiency degrader 913 canmodel the efficiency η_(i) of connected equipment 610 at each time stepi as a function of the maintenance decisions B_(main,i) and theequipment purchase decisions B_(cap,i). For example, the efficiencyη_(i) for a particular device may start at an initial value η₀ at thebeginning of the optimization period and may degrade over time such thatthe efficiency η_(i) decreases with each successive time step i.Performing maintenance on a device may reset the efficiency η_(i) to ahigher value immediately after the maintenance is performed. Similarly,purchasing a new device to replace an existing device may reset theefficiency η_(i) to a higher value immediately after the new device ispurchased. After being reset, the efficiency η_(i) may continue todegrade over time until the next time at which maintenance is performedor a new device is purchased.

Still referring to FIG. 9 , operational cost predictor 910 is shown toinclude a power consumption estimator 914 and an operational costcalculator 916. Power consumption estimator 914 can be configured toestimate the power consumption P_(op,i) of connected equipment 610 ateach time step i of the optimization period. In some embodiments, powerconsumption estimator 914 estimates the power consumption P_(op,i) as afunction of the ideal power consumption P_(ideal,i) calculated by idealperformance calculator 912 and the efficiency η_(i) determined byefficiency degrader 913 and/or efficiency updater 911. For example,power consumption estimator 914 can calculate the power consumptionP_(op,i) using the following equation:

$P_{{op},i} = \frac{P_{{ideal},i}}{\eta_{i}}$where P_(ideal,i) is the power consumption calculated by idealperformance calculator 912 based on the equipment performance curve forthe device at the corresponding load point Load_(i), and η_(i) is theoperating efficiency of the device at time step i.

In some embodiments, power consumption estimator 914 stores the powerconsumption values as an array P_(op) including an element for each ofthe h time steps in the optimization period. For example, powerconsumption estimator 914 can generate the following array:P _(op) =[P _(op,1) P _(op,2) . . . P _(op,h)]^(T)where the array P_(op) has a size of h×1 and each element of the arrayP_(op) includes a power consumption value P_(op,i) for a particular timestep i=1 . . . h of the optimization period.

Operational cost calculator 916 can be configured to estimate theoperational cost of connected equipment 610 over the duration of theoptimization period. In some embodiments, operational cost calculator916 calculates the operational cost during each time step i using thefollowing equation:Cost_(op,i) =C _(op,i) P _(op,i) Δtwhere P_(op,i) is the predicted power consumption at time step idetermined by power consumption estimator 914, C_(op,i) is the cost perunit of energy at time step i determined by energy costs module 915, andΔt is the duration of each time step. Operational cost calculator 916can sum the operational costs over the duration of the optimizationperiod as follows:

${Cost}_{op} = {\sum\limits_{i = 1}^{h}{Cost}_{{op},i}}$where Cost_(op) is the operational cost term of the objective functionJ.

In other embodiments, operational cost calculator 916 estimates theoperational cost Cost_(op) by multiplying the cost array C_(op) by thepower consumption array P_(op) and the duration of each time step Δt asshown in the following equations:Cost_(op) =C _(op) P _(op) ΔtCost_(op) =[C _(op,1) C _(op,2) . . . C _(op,h) ][P _(op,1) P _(op,2) .. . P _(op,h)]^(T) ΔtMaintenance Cost Predictor

Maintenance cost predictor 920 can be configured to formulate the secondterm in the objective function J. The second term in the objectivefunction J represents the cost of performing maintenance on connectedequipment 610 over the duration of the optimization period and is shownto include two variables or parameters (i.e., C_(main,i) andB_(main,i)). Maintenance cost predictor 920 is shown to include amaintenance estimator 922, a reliability estimator 924, a maintenancecost calculator 926, and a maintenance costs module 928.

Reliability estimator 924 can be configured to estimate the reliabilityof connected equipment 610 based on the equipment performanceinformation received from connected equipment 610. The reliability maybe a statistical measure of the likelihood that connected equipment 610will continue operating without fault under its current operatingconditions. Operating under more strenuous conditions (e.g., high load,high temperatures, etc.) may result in a lower reliability, whereasoperating under less strenuous conditions (e.g., low load, moderatetemperatures, etc.) may result in a higher reliability. In someembodiments, the reliability is based on an amount of time that haselapsed since connected equipment 610 last received maintenance and/oran amount of time that has elapsed since connected equipment 610 waspurchased or installed.

In some embodiments, reliability estimator 924 uses the equipmentperformance information to identify a current operating state ofconnected equipment 610. The current operating state can be examined byreliability estimator 924 to expose when connected equipment 610 beginsto degrade in performance and/or to predict when faults will occur. Insome embodiments, reliability estimator 924 estimates a likelihood ofvarious types of failures that could potentially occur in connectedequipment 610. The likelihood of each failure may be based on thecurrent operating conditions of connected equipment 610, an amount oftime that has elapsed since connected equipment 610 has been installed,and/or an amount of time that has elapsed since maintenance was lastperformed. In some embodiments, reliability estimator 924 identifiesoperating states and predicts the likelihood of various failures usingthe systems and methods described in U.S. patent application Ser. No.15/188,824 titled “Building Management System With PredictiveDiagnostics” and filed Jun. 21, 2016, the entire disclosure of which isincorporated by reference herein.

In some embodiments, reliability estimator 924 receives operating datafrom a plurality of devices of connected equipment 610 distributedacross multiple buildings. The operating data can include, for example,current operating conditions, fault indications, failure times, or otherdata that characterize the operation and performance of connectedequipment 610. Reliability estimator 924 can use the set of operatingdata to develop a reliability model for each type of equipment. Thereliability models can be used by reliability estimator 924 to estimatethe reliability of any given device of connected equipment 610 as afunction of its current operating conditions and/or other extraneousfactors (e.g., time since maintenance was last performed, time sinceinstallation or purchase, geographic location, water quality, etc.).

One example of a reliability model which can be used by reliabilityestimator 924 is shown in the following equation:Reliability_(i)=ƒ(OpCond_(i) ,Δt _(main,i) ,Δt _(cap,i))where Reliability_(i) is the reliability of connected equipment 610 attime step i, OpCond_(i) are the operating conditions at time step i,Δt_(main,i) is the amount of time that has elapsed between the time atwhich maintenance was last performed and time step i, and Δt_(cap,i) isthe amount of time that has elapsed between the time at which connectedequipment 610 was purchased or installed and time step i. Reliabilityestimator 924 can be configured to identify the current operatingconditions OpCond_(i) based on the equipment performance informationreceived as a feedback from connected equipment 610. Operating undermore strenuous conditions (e.g., high load, extreme temperatures, etc.)may result in a lower reliability, whereas operating under lessstrenuous conditions (e.g., low load, moderate temperatures, etc.) mayresult in a higher reliability.

Reliability estimator 924 may determine the amount of time Δt_(main,i)that has elapsed since maintenance was last performed on connectedequipment 610 based on the values of the binary decision variablesB_(main,i). For each time step i, reliability estimator 924 can examinethe corresponding values of B_(main) at time step i and each previoustime step (e.g., time steps i−1, i−2, . . . , 1). Reliability estimator924 can calculate the value of Δt_(main,i) by subtracting the time atwhich maintenance was last performed (i.e., the most recent time atwhich B_(main,i)=1) from the time associated with time step i. A longamount of time Δt_(main,i) since maintenance was last performed mayresult in a lower reliability, whereas a short amount of time sincemaintenance was last performed may result in a higher reliability.

Similarly, reliability estimator 924 may determine the amount of timeΔt_(cap,i) that has elapsed since connected equipment 610 was purchasedor installed based on the values of the binary decision variablesB_(cap,i). For each time step i, reliability estimator 924 can examinethe corresponding values of B_(cap) at time step i and each previoustime step (e.g., time steps i−1, i−2, . . . , 1). Reliability estimator924 can calculate the value of Δt_(cap,i) by subtracting the time atwhich connected equipment 610 was purchased or installed (i.e., the mostrecent time at which B_(cap,i)=1) from the time associated with timestep i. A long amount of time Δt_(cap,i) since connected equipment 610was purchased or installed may result in a lower reliability, whereas ashort amount of time since connected equipment 610 was purchased orinstalled may result in a higher reliability.

Reliability estimator 924 can be configured to reset the reliability fora given time step i if the binary decision variables B_(main,i) andB_(cap,i) indicate that maintenance will be performed at that time stepand/or new equipment will be purchased at that time step (i.e.,B_(main,i)=1 and/or B_(cap,i)=1). For example, if B_(main,i)=1,reliability estimator 924 can be configured to reset the value ofReliability to Reliability_(main,i), where Reliability_(main,i) is thereliability value that is expected to result from the maintenanceperformed at time step i. Similarly, if B_(cap,i)=1, reliabilityestimator 924 can be configured to reset the value of Reliability toReliability_(cap), where Reliability_(cap) is the reliability value thatis expected to result from purchasing a new device to supplement orreplace one or more devices of connected equipment 610 performed at timestep i. Reliability estimator 924 can dynamically reset the reliabilityfor one or more time steps while the optimization is being performed(e.g., with each iteration of the optimization) based on the values ofbinary decision variables B_(main,i) and B_(cap,i).

Maintenance estimator 922 can be configured to use the estimatedreliability of connected equipment 610 over the duration of theoptimization period to determine the probability that connectedequipment 610 will require maintenance and/or replacement at each timestep of the optimization period. In some embodiments, maintenanceestimator 922 is configured to compare the probability that connectedequipment 610 will require maintenance at a given time step to acritical value. Maintenance estimator 922 can be configured to set thevalue of B_(main,i)=1 in response to a determination that theprobability that connected equipment 610 will require maintenance attime step i exceeds the critical value. Similarly, maintenance estimator922 can be configured to compare the probability that connectedequipment 610 will require replacement at a given time step to acritical value. Maintenance estimator 922 can be configured to set thevalue of B_(cap,i)=1 in response to a determination that the probabilitythat connected equipment 610 will require replacement at time step iexceeds the critical value.

In some embodiments, a reciprocal relationship exists between thereliability of connected equipment 610 and the values of the binarydecision variables B_(main,i) and B_(cap,i). In other words, thereliability of connected equipment 610 can affect the values of thebinary decision variables B_(main,i) and B_(cap,i) selected in theoptimization, and the values of the binary decision variables B_(main,i)and B_(cap,i) can affect the reliability of connected equipment 610.Advantageously, the optimization performed by objective functionoptimizer 940 can identify the optimal values of the binary decisionvariables B_(main,i) and B_(cap,i) while accounting for the reciprocalrelationship between the binary decision variables B_(main,i) andB_(cap,i) and the reliability of connected equipment 610.

In some embodiments, maintenance estimator 922 generates a matrixB_(main) of the binary maintenance decision variables. The matrixB_(main) may include a binary decision variable for each of thedifferent maintenance activities that can be performed at each time stepof the optimization period. For example, maintenance estimator 922 cangenerate the following matrix:

$B_{main} = \begin{bmatrix}B_{{main},1,1} & B_{{main},1,2} & \ldots & B_{{main},1,h} \\B_{{main},2,1} & B_{{main},2,2} & \ldots & B_{{main},2,h} \\ \vdots & \vdots & \ddots & \vdots \\B_{{main},m,1} & B_{{main},m,2} & \ldots & B_{{main},m,h}\end{bmatrix}$where the matrix B_(main) has a size of m×h and each element of thematrix B_(main) includes a binary decision variable for a particularmaintenance activity at a particular time step of the optimizationperiod. For example, the value of the binary decision variableB_(main,j,i) indicates whether the jth maintenance activity will beperformed during the ith time step of the optimization period.

Still referring to FIG. 9 , maintenance cost predictor 920 is shown toinclude a maintenance costs module 928 and a maintenance costscalculator 926. Maintenance costs module 928 can be configured todetermine costs C_(main,i) associated with performing various types ofmaintenance on connected equipment 610. Maintenance costs module 928 canreceive a set of maintenance costs from an external system or device(e.g., a database, a user device, etc.). In some embodiments, themaintenance costs define the economic cost (e.g., $) of performingvarious types of maintenance. Each type of maintenance activity may havea different economic cost associated therewith. For example, themaintenance activity of changing the oil in a chiller compressor mayincur a relatively small economic cost, whereas the maintenance activityof completely disassembling the chiller and cleaning all of the chilledwater tubes may incur a significantly larger economic cost.

Maintenance costs module 928 can use the maintenance costs to define thevalues of C_(main) in objective function J. In some embodiments,maintenance costs module 928 stores the maintenance costs as an arrayC_(main) including a cost element for each of the maintenance activitiesthat can be performed. For example, maintenance costs module 928 cangenerate the following array:C _(main) =[C _(main,1) C _(main,2) . . . C _(main,m)]where the array C_(main) has a size of 1×m and each element of the arrayC_(main) includes a maintenance cost value C_(main,j) for a particularmaintenance activity j=1 . . . m.

Some maintenance activities may be more expensive than other. However,different types of maintenance activities may result in different levelsof improvement to the efficiency η and/or the reliability of connectedequipment 610. For example, merely changing the oil in a chiller mayresult in a minor improvement in efficiency η and/or a minor improvementin reliability, whereas completely disassembling the chiller andcleaning all of the chilled water tubes may result in a significantlygreater improvement to the efficiency η and/or the reliability ofconnected equipment 610. Accordingly, multiple different levels ofpost-maintenance efficiency (i.e., η_(main)) and post-maintenancereliability (i.e., Reliability_(main)) may exist. Each level of η_(main)and Reliability_(main) may correspond to a different type of maintenanceactivity.

In some embodiments, maintenance estimator 922 stores each of thedifferent levels of η_(main) and Reliability_(main) in a correspondingarray. For example, the parameter η_(main) can be defined as an arrayη_(main) with an element for each of the m different types ofmaintenance activities. Similarly, the parameter Reliability_(main) canbe defined as an array Reliability_(main) with an element for each ofthe m different types of maintenance activities. Examples of thesearrays are shown in the following equations:η_(main)=[η_(main,1)η_(main,2) . . . η_(main,m)]Reliability_(main)=[Reliability_(main,1) Reliability_(main,2) . . .Reliability_(main,m)]where the array η_(main) has a size of 1×m and each element of the arrayη_(main) includes a post-maintenance efficiency value η_(main,i) for aparticular maintenance activity. Similarly, the array Reliability_(main)has a size of 1×m and each element of the array Reliability_(main)includes a post-maintenance reliability value Reliability_(main,j) for aparticular maintenance activity.

In some embodiments, efficiency updater 911 identifies the maintenanceactivity associated with each binary decision variable B_(main,j,i) andresets the efficiency η to the corresponding post-maintenance efficiencylevel η_(main,j) if B_(main,j,i)=1. Similarly, reliability estimator 924can identify the maintenance activity associated with each binarydecision variable B_(main,j,i) and can reset the reliability to thecorresponding post-maintenance reliability level Reliability_(main,j) ifB_(main,j,i)=1.

Maintenance cost calculator 926 can be configured to estimate themaintenance cost of connected equipment 610 over the duration of theoptimization period. In some embodiments, maintenance cost calculator926 calculates the maintenance cost during each time step i using thefollowing equation:Cost_(main,i) =C _(main,i) B _(main,i)where C_(main,i) is an array of maintenance costs including an elementfor each of the m different types of maintenance activities that can beperformed at time step i and B_(main,i) is an array of binary decisionvariables indicating whether each of the m maintenance activities willbe performed at time step i. Maintenance cost calculator 926 can sum themaintenance costs over the duration of the optimization period asfollows:

${Cost}_{main} = {\sum\limits_{i = 1}^{h}{Cost}_{{main},i}}$where Cost_(main) is the maintenance cost term of the objective functionJ.

In other embodiments, maintenance cost calculator 926 estimates themaintenance cost Cost_(main) by multiplying the maintenance cost arrayC_(main) by the matrix of binary decision variables B_(main) as shown inthe following equations:

${{Cost}_{main} = {C_{main}B_{main}}}{{Cost}_{main} = {\begin{bmatrix}{\text{⁠}C_{{main},1}} & C_{{main},2} & \cdots & C_{{main},m}\end{bmatrix}{\left\lbrack \text{⁠}\begin{matrix}B_{{main},1,1} & B_{{main},1,2} & \cdots & B_{{main},1,h} \\B_{{main},2,1} & B_{{main},2,2} & \cdots & B_{{main},2,h} \\ \vdots & \vdots & \ddots & \vdots \\B_{{main},m,1} & B_{{main},m,2} & \cdots & B_{{main},m,h}\end{matrix}\text{⁠} \right\rbrack}}}$Capital Cost Predictor

Capital cost predictor 930 can be configured to formulate the third termin the objective function J. The third term in the objective function Jrepresents the cost of purchasing new devices of connected equipment 610over the duration of the optimization period and is shown to include twovariables or parameters (i.e., C_(cap,i) and B_(cap,i)). Capital costpredictor 930 is shown to include a purchase estimator 932, areliability estimator 934, a capital cost calculator 936, and a capitalcosts module 938.

Reliability estimator 934 can include some or all of the features ofreliability estimator 924, as described with reference to maintenancecost predictor 920. For example, reliability estimator 934 can beconfigured to estimate the reliability of connected equipment 610 basedon the equipment performance information received from connectedequipment 610. The reliability may be a statistical measure of thelikelihood that connected equipment 610 will continue operating withoutfault under its current operating conditions. Operating under morestrenuous conditions (e.g., high load, high temperatures, etc.) mayresult in a lower reliability, whereas operating under less strenuousconditions (e.g., low load, moderate temperatures, etc.) may result in ahigher reliability. In some embodiments, the reliability is based on anamount of time that has elapsed since connected equipment 610 lastreceived maintenance and/or an amount of time that has elapsed sinceconnected equipment 610 was purchased or installed. Reliabilityestimator 934 can include some or all of the features and/orfunctionality of reliability estimator 924, as previously described.

Purchase estimator 932 can be configured to use the estimatedreliability of connected equipment 610 over the duration of theoptimization period to determine the probability that new devices ofconnected equipment 610 will be purchased at each time step of theoptimization period. In some embodiments, purchase estimator 932 isconfigured to compare the probability that new devices of connectedequipment 610 will be purchased at a given time step to a criticalvalue. Purchase estimator 932 can be configured to set the value ofB_(cap,i)=1 in response to a determination that the probability thatconnected equipment 610 will be purchased at time step i exceeds thecritical value.

In some embodiments, purchase estimator 932 generates a matrix B_(cap)of the binary capital decision variables. The matrix B_(cap) may includea binary decision variable for each of the different capital purchasesthat can be made at each time step of the optimization period. Forexample, purchase estimator 932 can generate the following matrix:

$B_{cap} = {\left\lbrack \text{⁠}\begin{matrix}B_{{cap},1,1} & B_{{cap},1,2} & \cdots & B_{{cap},1,h} \\B_{{cap},2,1} & B_{{cap},2,2} & \cdots & B_{{cap},2,h} \\ \vdots & \vdots & \ddots & \vdots \\B_{{cap},p,1} & B_{{cap},p,2} & \cdots & B_{{cap},p,h}\end{matrix}\text{⁠} \right\rbrack}$where the matrix B_(cap) has a size of p×h and each element of thematrix B_(cap) includes a binary decision variable for a particularcapital purchase at a particular time step of the optimization period.For example, the value of the binary decision variable B_(cap,k,i)indicates whether the kth capital purchase will be made during the ithtime step of the optimization period.

Still referring to FIG. 9 , capital cost predictor 930 is shown toinclude a capital costs module 938 and a capital cost calculator 936.Capital costs module 938 can be configured to determine costs C_(cap,i)associated with various capital purchases (i.e., purchasing one or morenew devices of connected equipment 610). Capital costs module 938 canreceive a set of capital costs from an external system or device (e.g.,a database, a user device, etc.). In some embodiments, the capital costsdefine the economic cost (e.g., $) of making various capital purchases.Each type of capital purchase may have a different economic costassociated therewith. For example, purchasing a new temperature sensormay incur a relatively small economic cost, whereas purchasing a newchiller may incur a significantly larger economic cost.

Capital costs module 938 can use the purchase costs to define the valuesof C_(cap,i) in objective function J. In some embodiments, capital costsmodule 938 stores the capital costs as an array C_(cap) including a costelement for each of the capital purchases that can be made. For example,capital costs module 938 can generate the following array:C _(cap) =[C _(cap,1) C _(cap,2) . . . C _(cap,p)]where the array C_(cap) has a size of 1×p and each element of the arrayC_(cap) includes a cost value C_(cap,k) for a particular capitalpurchase k=1 . . . p.

Some capital purchases may be more expensive than other. However,different types of capital purchases may result in different levels ofimprovement to the efficiency η and/or the reliability of connectedequipment 610. For example, purchasing a new sensor to replace anexisting sensor may result in a minor improvement in efficiency η and/ora minor improvement in reliability, whereas purchasing a new chiller andcontrol system may result in a significantly greater improvement to theefficiency η and/or the reliability of connected equipment 610.Accordingly, multiple different levels of post-purchase efficiency(i.e., η_(cap)) and post-purchase reliability (i.e., Reliability_(cap))may exist. Each level of η_(cap) and Reliability_(cap) may correspond toa different type of capital purchase.

In some embodiments, purchase estimator 932 stores each of the differentlevels of η_(cap) and Reliability_(cap) in a corresponding array. Forexample, the parameter η_(cap) can be defined as an array η_(cap) withan element for each of the p different types of capital purchases whichcan be made. Similarly, the parameter Reliability_(cap) can be definedas an array Reliability_(cap) with an element for each of the pdifferent types of capital purchases that can be made. Examples of thesearrays are shown in the following equations:η_(cap)=[η_(cap,1)η_(cap,2) . . . η_(cap,p)]Reliability_(cap)=[Reliability_(cap,1) Reliability_(cap,2) . . .Reliability_(cap,p)]where the array η_(cap) has a size of 1×p and each element of the arrayη_(cap) includes a post-purchase efficiency value η_(cap,k) for aparticular capital purchase k. Similarly, the array Reliability_(cap)has a size of 1×p and each element of the array Reliability_(cap)includes a post-purchase reliability value Reliability_(cap,k) for aparticular capital purchase k.

In some embodiments, efficiency updater 911 identifies the capitalpurchase associated with each binary decision variable B_(main,k,i) andresets the efficiency η to the corresponding post-purchase efficiencylevel η_(cap,k) if B_(cap,k,i)=1. Similarly, reliability estimator 924can identify the capital purchase associated with each binary decisionvariable B_(cap,k,i) and can reset the reliability to the correspondingpost-purchase reliability level Reliability_(cap,k) if B_(main,k,i)=1.

Capital cost calculator 936 can be configured to estimate the capitalcost of connected equipment 610 over the duration of the optimizationperiod. In some embodiments, capital cost calculator 936 calculates thecapital cost during each time step i using the following equation:Cost_(cap,i) =C _(cap,i) B _(cap,i)where c_(cap,i) is an array of capital purchase costs including anelement for each of the p different capital purchases that can be madeat time step i and B_(cap,i) is an array of binary decision variablesindicating whether each of the p capital purchases will be made at timestep i. Capital cost calculator 936 can sum the capital costs over theduration of the optimization period as follows:

${Cost}_{cap} = {\sum\limits_{i = 1}^{h}{Cost}_{{cap},i}}$where Cost_(cap) is the capital cost term of the objective function J.

In other embodiments, capital cost calculator 936 estimates the capitalcost Cost_(cap) by multiplying the capital cost array C_(cap) by thematrix of binary decision variables B_(cap) as shown in the followingequations:

${{Cost}_{cap} = {C_{cap}B_{cap}}}{{Cost}_{cap} = {\begin{bmatrix}{\text{⁠}C_{{cap},1}} & C_{{cap},2} & \cdots & C_{{cap},p}\end{bmatrix}{\left\lbrack \text{⁠}\begin{matrix}B_{{cap},1,1} & B_{{cap},1,2} & \cdots & B_{{cap},1,h} \\B_{{cap},2,1} & B_{{cap},2,2} & \cdots & B_{{cap},2,h} \\ \vdots & \vdots & \ddots & \vdots \\B_{{cap},p,1} & B_{{cap},p,2} & \cdots & B_{{cap},p,h}\end{matrix}\text{⁠} \right\rbrack}}}$Objective Function Optimizer

Still referring to FIG. 9 , high level optimizer 832 is shown to includean objective function generator 935 and an objective function optimizer940. Objective function generator 935 can be configured to generate theobjective function J by summing the operational cost term, themaintenance cost term, and the capital cost term formulated by costpredictors 910, 920, and 930. One example of an objective function whichcan be generated by objective function generator 935 is shown in thefollowing equation:

$J = {{\sum\limits_{i = 1}^{h}{C_{{op},i}P_{{op},i}{\Delta t}}} + {\sum\limits_{i = 1}^{h}{C_{{main},i}B_{{main},i}}} + {\sum\limits_{i = 1}^{h}{C_{{cap},i}B_{{cap},i}}}}$where C_(op,i) is the cost per unit of energy (e.g., $/kWh) consumed byconnected equipment 610 at time step i of the optimization period,P_(op,i) is the power consumption (e.g., kW) of connected equipment 610at time step i, Δt is the duration of each time step i, C_(main,i) isthe cost of maintenance performed on connected equipment 610 at timestep i, B_(main,i) is a binary variable that indicates whether themaintenance is performed, C_(cap,i) is the capital cost of purchasing anew device of connected equipment 610 at time step i, B_(cap,i) is abinary variable that indicates whether the new device is purchased, andh is the duration of the horizon or optimization period over which theoptimization is performed.

Another example of an objective function which can be generated byobjective function generator 935 is shown in the following equation:

${J = {{C_{op}P_{op}{\Delta t}} + {C_{main}B_{main}} + {C_{cap}B_{cap}}}}{J = {{{\begin{bmatrix}{\text{⁠}C_{{op},1}} & C_{{op},2} & \ldots & C_{{op},h}\end{bmatrix}\begin{bmatrix}{\text{⁠}P_{{op},1}} & P_{{op},2} & \cdots & P_{{op},h}\end{bmatrix}}^{T}{\Delta t}} + {{\begin{bmatrix}{\text{⁠}C_{{main},1}} & C_{{main},2} & \cdots & C_{{main},m}\end{bmatrix}\text{⁠}{{\left\lbrack \text{⁠}\begin{matrix}B_{{main},1,1} & B_{{main},1,2} & \cdots & B_{{main},1,h} \\B_{{main},2,1} & B_{{main},2,2} & \cdots & B_{{main},2,h} \\ \vdots & \vdots & \ddots & \vdots \\B_{{main},m,1} & B_{{main},m,2} & \cdots & B_{{main},m,h}\end{matrix}\text{⁠} \right\rbrack + {{\left\lbrack {\begin{matrix}{\text{⁠}C_{{cap},1}} & C_{{cap},2} & \cdots & C_{{cap},p}\end{matrix}} \right\rbrack{\left\lbrack \text{⁠}\begin{matrix}B_{{cap},1,1} & B_{{cap},1,2} & \cdots & B_{{cap},1,h} \\B_{{cap},2,1} & B_{{cap},2,2} & \cdots & B_{{cap},2,h} \\ \vdots & \vdots & \ddots & \vdots \\B_{{cap},p,1} & B_{{cap},p,2} & \cdots & B_{{cap},p,h}\end{matrix}\text{⁠} \right\rbrack}}}}}}}}}$where the array C_(op) includes an energy cost value C_(op,i) for aparticular time step i=1 . . . h of the optimization period, the arrayP_(op) includes a power consumption value P_(op,i) for a particular timestep i=1 . . . h of the optimization period, each element of the arrayC_(main) includes a maintenance cost value c_(main,j) for a particularmaintenance activity j=1 . . . m, each element of the matrix B_(main)includes a binary decision variable for a particular maintenanceactivity j=1 . . . m at a particular time step i=1 . . . h of theoptimization period, each element of the array C_(cap) includes acapital cost value C_(cap,k) for a particular capital purchase k=1 . . .p, and each element of the matrix B_(cap) includes a binary decisionvariable for a particular capital purchase k=1 . . . p at a particulartime step i=1 . . . h of the optimization period.

Objective function generator 935 can be configured to impose constraintson one or more variables or parameters in the objective function J. Theconstraints can include any of the equations or relationships describedwith reference to operational cost predictor 910, maintenance costpredictor 920, and capital cost predictor 930. For example, objectivefunction generator 935 can impose a constraint which defines the powerconsumption values P_(op,i) for one or more devices of connectedequipment 610 as a function of the ideal power consumption P_(ideal,i)and the efficiency η_(i) (e.g., P_(op,i)=P_(ideal,i)/η_(i)). Objectivefunction generator 935 can impose a constraint which defines theefficiency η_(i) as a function of the binary decision variablesB_(main,i) and B_(cap,i), as described with reference to efficiencyupdater 911 and efficiency degrader 913. Objective function generator935 can impose a constraint which constrains the binary decisionvariables B_(main,i) and B_(cap,i) to a value of either zero or one anddefines the binary decision variables B_(main,i) and B_(cap,i) as afunction of the reliability Reliability_(i) of connected equipment 610,as described with reference to maintenance estimator 922 and purchaseestimator 932. Objective function generator 935 can impose a constraintwhich defines the reliability Reliability_(i) of connected equipment 610as a function of the equipment performance information (e.g., operatingconditions, run hours, etc.) as described with reference to reliabilityestimators 924 and 934.

Objective function optimizer 940 can optimize the objective function Jto determine the optimal values of the binary decision variablesB_(main,i) and B_(cap,i) over the duration of the optimization period.Objective function optimizer 940 can use any of a variety ofoptimization techniques to formulate and optimize the objective functionJ. For example, objective function optimizer 940 can use integerprogramming, mixed integer linear programming, stochastic optimization,convex programming, dynamic programming, or any other optimizationtechnique to formulate the objective function J, define the constraints,and perform the optimization. These and other optimization techniquesare known in the art and will not be described in detail here.

In some embodiments, objective function optimizer 940 uses mixed integerstochastic optimization to optimize the objective function J. In mixedinteger stochastic optimization, some of the variables in the objectivefunction J can be defined as functions of random variables orprobabilistic variables. For example, the decision variables B_(main,i)and B_(cap,i) can be defined as binary variables that have probabilisticvalues based on the reliability of connected equipment 610. Lowreliability values may increase the probability that the binary decisionvariables B_(main,i) and B_(cap,i) will have a value of one (e.g.,B_(main,i)=1 and B_(cap,i)=1), whereas high reliability values mayincrease the probability that the binary decision variables B_(main,i)and B_(cap,i) will have a value of zero (e.g., B_(main,i)=0 andB_(cap,i)=0). In some embodiments, maintenance estimator 922 andpurchase estimator 932 use a mixed integer stochastic technique todefine the values of the binary decision variables B_(main,i) andB_(cap,i) as a probabilistic function of the reliability of connectedequipment 610.

As discussed above, the objective function J may represent the predictedcost of operating, maintaining, and purchasing one or more devices ofconnected equipment 610 over the duration of the optimization period. Insome embodiments, objective function optimizer 940 is configured toproject these costs back to a particular point in time (e.g., thecurrent time) to determine the net present value (NPV) of the one ormore devices of connected equipment 610 at a particular point in time.For example, objective function optimizer 940 can project each of thecosts in objective function J back to the current time using thefollowing equation:

${NPV}_{cost} = {\sum\limits_{i = 1}^{h}\frac{{Cost}_{i}}{\left( {1 + r} \right)^{i}}}$where r is the interest rate, Cost is the cost incurred during time stepi of the optimization period, and NPV_(cost) is the net present value(i.e., the present cost) of the total costs incurred over the durationof the optimization period. In some embodiments, objective functionoptimizer 940 optimizes the net present value NPV_(cost) to determinethe NPV of one or more devices of connected equipment 610 at aparticular point in time.

As discussed above, one or more variables or parameters in the objectivefunction J can be updated dynamically based on closed-loop feedback fromconnected equipment 610. For example, the equipment performanceinformation received from connected equipment 610 can be used to updatethe reliability and/or the efficiency of connected equipment 610.Objective function optimizer 940 can be configured to optimize theobjective function J periodically (e.g., once per day, once per week,once per month, etc.) to dynamically update the predicted cost and/orthe net present value NPV_(cost) based on the closed-loop feedback fromconnected equipment 610.

In some embodiments, objective function optimizer 940 generatesoptimization results. The optimization results may include the optimalvalues of the decision variables in the objective function J for eachtime step i in the optimization period. The optimization results includeoperating decisions, equipment maintenance decisions, and/or equipmentpurchase decisions for each device of connected equipment 610. In someembodiments, the optimization results optimize the economic value ofoperating, maintaining, and purchasing connected equipment 610 over theduration of the optimization period. In some embodiments, theoptimization results optimize the net present value of one or moredevices of connected equipment 610 at a particular point in time. Theoptimization results may cause BMS 606 to activate, deactivate, oradjust a setpoint for connected equipment 610 in order to achieve theoptimal values of the decision variables specified in the optimizationresults.

In some embodiments, MPM system 602 uses the optimization results togenerate equipment purchase and maintenance recommendations. Theequipment purchase and maintenance recommendations may be based on theoptimal values for the binary decision variables B_(main,i) andB_(cap,i) determined by optimizing the objective function J. Forexample, a value of B_(main,25)=1 for a particular device of connectedequipment 610 may indicate that maintenance should be performed on thatdevice at the 25^(th) time step of the optimization period, whereas avalue of B_(main,25)=0 may indicate that the maintenance should not beperformed at that time step. Similarly, a value of B_(cap,25)=1 mayindicate that a new device of connected equipment 610 should bepurchased at the 25^(th) time step of the optimization period, whereas avalue of B_(cap,25)=0 may indicate that the new device should not bepurchased at that time step.

In some embodiments, the equipment purchase and maintenancerecommendations are provided to building 10 (e.g., to BMS 606) and/or toclient devices 448. An operator or building owner can use the equipmentpurchase and maintenance recommendations to assess the costs andbenefits of performing maintenance and purchasing new devices. In someembodiments, the equipment purchase and maintenance recommendations areprovided to service technicians 620. Service technicians 620 can use theequipment purchase and maintenance recommendations to determine whencustomers should be contacted to perform service or replace equipment.

Model Predictive Maintenance Process

Referring now to FIG. 10 , a flowchart of a model predictive maintenanceprocess 1000 is shown, according to an exemplary embodiment. Process1000 can be performed by one or more components of building system 600.In some embodiments, process 1000 is performed by MPM system 602, asdescribed with reference to FIGS. 6-9 .

Process 1000 is shown to include operating building equipment to affecta variable state or condition of a building (step 1002) and receivingequipment performance information as feedback from the buildingequipment (step 1004). The building equipment can include type ofequipment which can be used to monitor and/or control a building (e.g.,connected equipment 610). For example, the building equipment caninclude chillers, AHUs, boilers, batteries, heaters, economizers,valves, actuators, dampers, cooling towers, fans, pumps, lightingequipment, security equipment, refrigeration equipment, or any othertype of equipment in a building system or building management system.The building equipment can include any of the equipment of HVAC system100, waterside system 200, airside system 300, BMS 400, and/or BMS 500,as described with reference to FIGS. 1-5 . The equipment performanceinformation can include samples of monitored variables (e.g., measuredtemperature, measured pressure, measured flow rate, power consumption,etc.), current operating conditions (e.g., heating or cooling load,current operating state, etc.), fault indications, or other types ofinformation that characterize the performance of the building equipment.

Process 1000 is shown to include estimating an efficiency andreliability of the building equipment as a function of the equipmentperformance information (step 1006). In some embodiments, step 1006 isperformed by efficiency updater 911 and reliability estimators 924, 926as described with reference to FIG. 9 . Step 1006 can include using theequipment performance information to determine the efficiency η of thebuilding equipment under actual operating conditions. In someembodiments, the efficiency η_(i) represents the ratio of the idealpower consumption P_(ideal) of the building equipment to the actualpower consumption P actual of the building equipment, as shown in thefollowing equation:

$\eta = \frac{P_{ideal}}{P_{actual}}$where P_(ideal) is the ideal power consumption of the building equipmentas defined by the performance curve for the building equipment andP_(actual) is the actual power consumption of the building equipment. Insome embodiments, step 1006 includes using the equipment performanceinformation collected in step 1002 to identify the actual powerconsumption value P_(actual). Step 1006 can include using the actualpower consumption P_(actual) in combination with the ideal powerconsumption P_(ideal) to calculate the efficiency η.

Step 1006 can include periodically updating the efficiency η to reflectthe current operating efficiency of the building equipment. For example,step 1006 can include calculating the efficiency η of the buildingequipment once per day, once per week, once per year, or at any otherinterval as may be suitable to capture changes in the efficiency η overtime. Each value of the efficiency η may be based on correspondingvalues of P_(ideal) and P_(actual) at the time the efficiency η iscalculated. In some embodiments, step 1006 includes updating theefficiency η each time the high level optimization process is performed(i.e., each time the objective function J is optimized). The efficiencyvalue calculated in step 1006 may be stored in memory 810 as an initialefficiency value η₀, where the subscript 0 denotes the value of theefficiency η at or before the beginning of the optimization period(e.g., at time step 0).

Step 1006 can include predicting the efficiency η_(i) of the buildingequipment at each time step i of the optimization period. The initialefficiency η₀ at the beginning of the optimization period may degradeover time as the building equipment degrade in performance. For example,the efficiency of a chiller may degrade over time as a result of thechilled water tubes becoming dirty and reducing the heat transfercoefficient of the chiller. Similarly, the efficiency of a battery maydecrease over time as a result of degradation in the physical orchemical components of the battery. Step 1006 can account for suchdegradation by incrementally reducing the efficiency η_(i) over theduration of the optimization period.

In some embodiments, the initial efficiency value η₀ is updated at thebeginning of each optimization period. However, the efficiency η maydegrade during the optimization period such that the initial efficiencyvalue η₀ becomes increasingly inaccurate over the duration of theoptimization period. To account for efficiency degradation during theoptimization period, step 1006 can include decreasing the efficiency ηby a predetermined amount with each successive time step. For example,step 1006 can include defining the efficiency at each time step i=1 h asfollows:η_(i)=η_(i-1)−Δηwhere η_(i) is the efficiency at time step i, η_(i-1) is the efficiencyat time step i−1, and Δη is the degradation in efficiency betweenconsecutive time steps. In some embodiments, this definition of η_(i) isapplied to each time step for which B_(main,i)=0 and B_(cap,i)=0.However, if either B_(main,i)=1 or B_(cap,i)=1, the value of η_(i) maybe reset to either η_(main) or η_(cap) in step 1018.

In some embodiments, the value of Δη is based on a time series ofefficiency values. For example, step 1006 may include recording a timeseries of the initial efficiency values η₀, where each of the initialefficiency values η₀ represents the empirically-calculated efficiency ofthe building equipment at a particular time. Step 1006 can includeexamining the time series of initial efficiency values η₀ to determinethe rate at which the efficiency degrades. For example, if the initialefficiency η₀ at time t₁ is η_(0,1) and the initial efficiency at timet₂ is η_(0.2), the rate of efficiency degradation can be calculated asfollows:

$\frac{\Delta\eta}{\Delta t} = {\frac{\eta_{0,2} - \eta_{0,1}}{t_{2} - t_{1}}{where}\frac{\Delta\eta}{\Delta t}}$is the rate of efficiency degradation. Step 1006 can include multiplying

$\frac{\Delta\eta}{\Delta t}$by the duration of each time step Δt to calculate the value of Δη

$\left( {{i.e.},{{\Delta\eta} = {\frac{\Delta\eta}{\Delta t}*{\Delta t}}}} \right).$

Step 1006 can include estimating the reliability of the buildingequipment based on the equipment performance information received instep 1004. The reliability may be a statistical measure of thelikelihood that the building equipment will continue operating withoutfault under its current operating conditions. Operating under morestrenuous conditions (e.g., high load, high temperatures, etc.) mayresult in a lower reliability, whereas operating under less strenuousconditions (e.g., low load, moderate temperatures, etc.) may result in ahigher reliability. In some embodiments, the reliability is based on anamount of time that has elapsed since the building equipment lastreceived maintenance and/or an amount of time that has elapsed since thebuilding equipment were purchased or installed.

In some embodiments, step 1006 includes using the equipment performanceinformation to identify a current operating state of the buildingequipment. The current operating state can be examined to expose whenthe building equipment begin to degrade in performance and/or to predictwhen faults will occur. In some embodiments, step 1006 includesestimating a likelihood of various types of failures that couldpotentially occur the building equipment. The likelihood of each failuremay be based on the current operating conditions of the buildingequipment, an amount of time that has elapsed since the buildingequipment have been installed, and/or an amount of time that has elapsedsince maintenance was last performed. In some embodiments, step 1006includes identifying operating states and predicts the likelihood ofvarious failures using the systems and methods described in U.S. patentapplication Ser. No. 15/188,824 titled “Building Management System WithPredictive Diagnostics” and filed Jun. 21, 2016, the entire disclosureof which is incorporated by reference herein.

In some embodiments, step 1006 includes receiving operating data frombuilding equipment distributed across multiple buildings. The operatingdata can include, for example, current operating conditions, faultindications, failure times, or other data that characterize theoperation and performance of the building equipment. Step 1006 caninclude using the set of operating data to develop a reliability modelfor each type of equipment. The reliability models can be used in step1006 to estimate the reliability of any given device of the buildingequipment as a function of its current operating conditions and/or otherextraneous factors (e.g., time since maintenance was last performed,time since installation or purchase, geographic location, water quality,etc.).

One example of a reliability model which can be used in step 1006 isshown in the following equation:Reliability_(i)=ƒ(OpCond_(i) ,Δt _(main,i) ,Δt _(cap,i))where Reliability_(i) is the reliability of the building equipment attime step i, OpCond_(i) are the operating conditions at time step i,Δt_(main,i) is the amount of time that has elapsed between the time atwhich maintenance was last performed and time step i, and Δt_(cap,i) isthe amount of time that has elapsed between the time at which thebuilding equipment were purchased or installed and time step i. Step1006 can include identifying the current operating conditions OpCond_(i)based on the equipment performance information received as a feedbackfrom the building equipment. Operating under more strenuous conditions(e.g., high load, extreme temperatures, etc.) may result in a lowerreliability, whereas operating under less strenuous conditions (e.g.,low load, moderate temperatures, etc.) may result in a higherreliability.

Still referring to FIG. 10 , process 1000 is shown to include predictingan energy consumption of the building equipment over an optimizationperiod as a function of the estimated efficiency (step 1008). In someembodiments, step 1008 is performed by ideal performance calculator 912and/or power consumption estimator, as described with reference to FIG.9 . Step 1008 can include receiving load predictions Load_(i) fromload/rate predictor 822 and performance curves from low level optimizer834. As discussed above, the performance curves may define the idealpower consumption P_(ideal) of the building equipment a function of theheating or cooling load on the device or set of devices. For example,the performance curve for the building equipment can be defined by thefollowing equation:P _(ideal,i)=ƒ(Load_(i))where P_(ideal,i) is the ideal power consumption (e.g., kW) of thebuilding equipment at time step i and Load_(i) is the load (e.g., tonscooling, kW heating, etc.) on the building equipment at time step i. Theideal power consumption P_(ideal,i) may represent the power consumptionof the building equipment assuming they operate at perfect efficiency.Step 1008 can include using the performance curve for the buildingequipment to identify the value of P_(ideal,i) that corresponds to theload point Load_(i) for the building equipment at each time step of theoptimization period.

In some embodiments, step 1008 includes estimating the power consumptionP_(op,i) as a function of the ideal power consumption P_(ideal,i) andthe efficiency η_(i) of the building equipment. For example, step 1008can include calculating the power consumption P_(op,i) using thefollowing equation:

$P_{{op},i} = \frac{P_{{ideal},i}}{\eta_{i}}$where P_(ideal,i) is the power consumption based on the equipmentperformance curve for the building equipment at the corresponding loadpoint Load_(i), and η_(i) is the operating efficiency of the buildingequipment at time step i.

Still referring to FIG. 10 , process 1000 is shown to include defining acost Cost_(op) of operating the building equipment over the optimizationperiod as a function of the predicted energy consumption (step 1010). Insome embodiments, step 1010 is performed by operational cost calculator916, as described with reference to FIG. 9 . Step 1010 can includecalculating the operational cost during each time step i using thefollowing equation:Cost_(op,i) =C _(op,i) P _(op,i) Δtwhere P_(op,i) is the predicted power consumption at time step idetermined in step 1008, C_(op,i) is the cost per unit of energy at timestep i, and Δt is the duration of each time step. Step 1010 can includesumming the operational costs over the duration of the optimizationperiod as follows:

${Cost}_{op} = {\sum\limits_{i = 1}^{h}{Cost}_{{op},i}}$where Cost_(op) is the operational cost term of the objective functionJ.

In other embodiments, step 1010 can include calculating the operationalcost Cost_(op) by multiplying the cost array C_(op) by the powerconsumption array P_(op) and the duration of each time step Δt as shownin the following equations:Cost_(op) =C _(op) P _(op) ΔtCost_(op) =[c _(op,1) C _(op,2) . . . c _(op,h) ][P _(op,1) P _(op,2) .. . P _(op,h)]^(T) Δtwhere the array C_(op) includes an energy cost value C_(op,i) for aparticular time step i=1 . . . h of the optimization period, the arrayP_(op) includes a power consumption value P_(op,i) for a particular timestep i=1 . . . h of the optimization period.

Still referring to FIG. 10 , process 1000 is shown to include defining acost of performing maintenance on the building equipment over theoptimization period as a function of the estimated reliability (step1012). Step 1012 can be performed by maintenance cost predictor 920, asdescribed with reference to FIG. 9 . Step 1012 can include using theestimated reliability of the building equipment over the duration of theoptimization period to determine the probability that the buildingequipment will require maintenance and/or replacement at each time stepof the optimization period. In some embodiments, step 1012 includescomparing the probability that the building equipment will requiremaintenance at a given time step to a critical value. Step 1012 caninclude setting the value of B_(main,i)=1 in response to a determinationthat the probability that the building equipment will requiremaintenance at time step i exceeds the critical value. Similarly, step1012 can include comparing the probability that the building equipmentwill require replacement at a given time step to a critical value. Step1012 can include setting the value of B_(cap,i)=1 in response to adetermination that the probability that the building equipment willrequire replacement at time step i exceeds the critical value.

Step 1012 can include determining the costs C_(main,i) associated withperforming various types of maintenance on the building equipment. Step1012 can include receiving a set of maintenance costs from an externalsystem or device (e.g., a database, a user device, etc.). In someembodiments, the maintenance costs define the economic cost (e.g., $) ofperforming various types of maintenance. Each type of maintenanceactivity may have a different economic cost associated therewith. Forexample, the maintenance activity of changing the oil in a chillercompressor may incur a relatively small economic cost, whereas themaintenance activity of completely disassembling the chiller andcleaning all of the chilled water tubes may incur a significantly largereconomic cost. Step 1012 can include using the maintenance costs todefine the values of C_(main,i) in objective function J.

Step 1012 can include estimating the maintenance cost of the buildingequipment over the duration of the optimization period. In someembodiments, step 1012 includes calculating the maintenance cost duringeach time step i using the following equation:Cost_(main,i) =C _(main,i) B _(main,i)where C_(main,i) is an array of maintenance costs including an elementfor each of the m different types of maintenance activities that can beperformed at time step i and B_(main,i) is an array of binary decisionvariables indicating whether each of the m maintenance activities willbe performed at time step i. Step 1012 can include summing themaintenance costs over the duration of the optimization period asfollows:

${Cost}_{main} = {\sum\limits_{i = 1}^{h}{Cost}_{{main},i}}$where Cost_(main) is the maintenance cost term of the objective functionJ.

In other embodiments, step 1012 includes estimating the maintenance costCost_(main) by multiplying the maintenance cost array C_(main) by thematrix of binary decision variables B_(main) as shown in the followingequations:

${{Cost}_{main} = {C_{main}B_{main}}}{{Cost}_{main} = {\begin{bmatrix}{\text{⁠}C_{{main},1}} & C_{{main},2} & \cdots & C_{{main},m}\end{bmatrix}{\left\lbrack \text{⁠}\begin{matrix}B_{{main},1,1} & B_{{main},1,2} & \cdots & B_{{main},1,h} \\B_{{main},2,1} & B_{{main},2,2} & \cdots & B_{{main},2,h} \\ \vdots & \vdots & \ddots & \vdots \\B_{{main},m,1} & B_{{main},m,2} & \cdots & B_{{main},m,h}\end{matrix}\text{⁠} \right\rbrack}}}$where each element of the array C_(main) includes a maintenance costvalue C_(main,j) for a particular maintenance activity j=1 . . . m andeach element of the matrix B_(main) includes a binary decision variablefor a particular maintenance activity j=1 . . . m at a particular timestep i=1 . . . h of the optimization period.

Still referring to FIG. 10 , process 1000 is shown to include defining acost Cost_(cap) of purchasing or replacing the building equipment overthe optimization period as a function of the estimated reliability (step1014). Step 1014 can be performed by capital cost predictor 930, asdescribed with reference to FIG. 9 . In some embodiments, step 1014includes using the estimated reliability of the building equipment overthe duration of the optimization period to determine the probabilitythat new devices of the building equipment will be purchased at eachtime step of the optimization period. In some embodiments, step 1014includes comparing the probability that new devices of the buildingequipment will be purchased at a given time step to a critical value.Step 1014 can include setting the value of B_(cap,i)=1 in response to adetermination that the probability that the building equipment will bepurchased at time step i exceeds the critical value.

Step 1014 can include determining the costs C_(cap,i) associated withvarious capital purchases (i.e., purchasing one or more new devices ofthe building equipment). Step 1014 can include receiving a set ofcapital costs from an external system or device (e.g., a database, auser device, etc.). In some embodiments, the capital costs define theeconomic cost (e.g., $) of making various capital purchases. Each typeof capital purchase may have a different economic cost associatedtherewith. For example, purchasing a new temperature sensor may incur arelatively small economic cost, whereas purchasing a new chiller mayincur a significantly larger economic cost. Step 1014 can include usingthe purchase costs to define the values of C_(cap,i) in objectivefunction J.

Some capital purchases may be more expensive than other. However,different types of capital purchases may result in different levels ofimprovement to the efficiency η and/or the reliability of the buildingequipment. For example, purchasing a new sensor to replace an existingsensor may result in a minor improvement in efficiency η and/or a minorimprovement in reliability, whereas purchasing a new chiller and controlsystem may result in a significantly greater improvement to theefficiency η and/or the reliability of the building equipment.Accordingly, multiple different levels of post-purchase efficiency(i.e., η_(cap)) and post-purchase reliability (i.e., Reliability_(cap))may exist. Each level of η_(cap) and Reliability_(cap) may correspond toa different type of capital purchase.

Step 1014 can include estimating the capital cost of the buildingequipment over the duration of the optimization period. In someembodiments, step 1014 includes calculating the capital cost during eachtime step i using the following equation:Cost_(cap,i) =C _(cap,i) B _(cap,i)where c_(cap,i) is an array of capital purchase costs including anelement for each of the p different capital purchases that can be madeat time step i and B_(cap,i) is an array of binary decision variablesindicating whether each of the p capital purchases will be made at timestep i. Step 1014 can include summing the capital costs over theduration of the optimization period as follows:

${Cost}_{cap} = {\sum\limits_{i = 1}^{h}{Cost}_{{cap},i}}$where Cost_(cap) is the capital cost term of the objective function J.

In other embodiments, step 1014 includes estimating the capital costCost_(cap) by multiplying the capital cost array C_(cap) by the matrixof binary decision variables B_(cap) as shown in the followingequations:

${{Cost}_{cap} = {C_{cap}B_{cap}}}{{Cost}_{cap} = {\left\lbrack {C_{{cap},1}C_{{cap},2}\cdots C_{{cap},p}} \right\rbrack\begin{bmatrix}B_{{cap},1,1} & B_{{cap},1,2} & \cdots & B_{{cap},1,h} \\B_{{cap},2,1} & B_{{cap},2,2} & \cdots & B_{{cap},2,h} \\ \vdots & \vdots & \ddots & \vdots \\B_{{cap},p,1} & B_{{cap},p,2} & \cdots & B_{{cap},p,h}\end{bmatrix}}}$where each element of the array C_(cap) includes a capital cost valueC_(cap,k) for a particular capital purchase k=1 . . . p and each elementof the matrix B_(cap) includes a binary decision variable for aparticular capital purchase k=1 . . . p at a particular time step i=1 .. . h of the optimization period.

Still referring to FIG. 10 , process 1000 is shown to include optimizingan objective function including the costs Cost_(op), Cost_(main), andCost_(cap) to determine an optimal maintenance strategy for the buildingequipment (step 1016). Step 1016 can include generating the objectivefunction J by summing the operational cost term, the maintenance costterm, and the capital cost term formulated in steps 1010-1014. Oneexample of an objective function which can be generated in step 1016 isshown in the following equation:

$J = {{\sum\limits_{i = 1}^{h}{C_{{op},i}P_{{op},i}\Delta t}} + {\sum\limits_{i = 1}^{h}{C_{{main},i}B_{{main},i}}} + {\sum\limits_{i = 1}^{h}{C_{{cap},i}B_{{cap},i}}}}$where C_(op,i) is the cost per unit of energy (e.g., $/kWh) consumed byconnected equipment 610 at time step i of the optimization period,P_(op,i) is the power consumption (e.g., kW) of connected equipment 610at time step i, Δt is the duration of each time step i, C_(main,i) isthe cost of maintenance performed on connected equipment 610 at timestep i, B_(main,i) is a binary variable that indicates whether themaintenance is performed, C_(cap,i) is the capital cost of purchasing anew device of connected equipment 610 at time step i, B_(cap,i) is abinary variable that indicates whether the new device is purchased, andh is the duration of the horizon or optimization period over which theoptimization is performed.

Another example of an objective function which can be generated in step1016 is shown in the following equation:

${J = {{C_{op}P_{op}\Delta t} + {C_{main}B_{main}} + {C_{cap}B_{cap}}}}{J = {{{\left\lbrack {C_{{op},1}C_{{op},2}\cdots C_{{op},h}} \right\rbrack\left\lbrack {P_{{op},1}P_{{op},2}\cdots P_{{op},h}} \right\rbrack}^{T}\Delta t} + {{{}\left\lbrack {C_{{main},1}C_{{main},2}\cdots\text{⁠⁠}C_{{main},m}} \right\rbrack}\left\lbrack \text{⁠}\begin{matrix}B_{{main},1,1} & B_{{main},1,2} & \cdots & B_{{main},1,h} \\B_{{main},2,1} & B_{{main},2,2} & \cdots & B_{{main},2,h} \\ \vdots & \vdots & \ddots & \vdots \\B_{{main},m,1} & B_{{maim},m,2} & \cdots & B_{{main},m,h}\end{matrix} \right\rbrack} + {{\left\lbrack \text{⁠}{C_{{cap},1}\text{⁠ ⁠}C_{{cap},2}\cdots C_{{cap},p}} \right\rbrack\begin{bmatrix}B_{{cap},1,1} & B_{{cap},1,2} & \cdots & B_{{cap},1,h} \\B_{{cap},2,1} & B_{{cap},2,2} & \cdots & B_{{main},2,} \\ \vdots & \vdots & \ddots & \vdots \\B_{{cap},p,1} & B_{{cap},p,2} & \cdots & B_{{cap},p,h}\end{bmatrix}}}}}$where the array C_(op) includes an energy cost value c_(op,i) for aparticular time step i=1 . . . h of the optimization period, the arrayP_(op) includes a power consumption value P_(op,i) for a particular timestep i=1 . . . h of the optimization period, each element of the arrayC_(main) includes a maintenance cost value C_(main,j) for a particularmaintenance activity j=1 . . . m, each element of the matrix B_(main)includes a binary decision variable for a particular maintenanceactivity j=1 . . . m at a particular time step i=1 . . . h of theoptimization period, each element of the array C_(cap) includes acapital cost value C_(cap,k) for a particular capital purchase k=1 . . .p, and each element of the matrix B_(cap) includes a binary decisionvariable for a particular capital purchase k=1 . . . p at a particulartime step i=1 . . . h of the optimization period.

Step 1016 can include imposing constraints on one or more variables orparameters in the objective function J. The constraints can include anyof the equations or relationships described with reference tooperational cost predictor 910, maintenance cost predictor 920, andcapital cost predictor 930. For example, step 1016 can include imposinga constraint which defines the power consumption values P_(op,i) for oneor more devices of the building equipment as a function of the idealpower consumption P_(ideal,i) and the efficiency η_(i) (e.g.,P_(op,i)=P_(ideal,i)/η_(i)). Step 1016 can include imposing a constraintwhich defines the efficiency η_(i) as a function of the binary decisionvariables B_(main,i) and B_(cap,i), as described with reference toefficiency updater 911 and efficiency degrader 913. Step 1016 caninclude imposing a constraint which constrains the binary decisionvariables B_(main,i) and B_(cap,i) to a value of either zero or one anddefines the binary decision variables B_(main,i) and B_(cap,i) as afunction of the reliability Reliability_(i) of connected equipment 610,as described with reference to maintenance estimator 922 and purchaseestimator 932. Step 1016 can include imposing a constraint which definesthe reliability Reliability_(i) of connected equipment 610 as a functionof the equipment performance information (e.g., operating conditions,run hours, etc.) as described with reference to reliability estimators924 and 934.

Step 1016 can include optimizing the objective function J to determinethe optimal values of the binary decision variables B_(main,i) andB_(cap,i) over the duration of the optimization period. Step 1016 caninclude using any of a variety of optimization techniques to formulateand optimize the objective function J. For example, step 1016 caninclude using integer programming, mixed integer linear programming,stochastic optimization, convex programming, dynamic programming, or anyother optimization technique to formulate the objective function J,define the constraints, and perform the optimization. These and otheroptimization techniques are known in the art and will not be describedin detail here.

In some embodiments, step 1016 includes using mixed integer stochasticoptimization to optimize the objective function J. In mixed integerstochastic optimization, some of the variables in the objective functionJ can be defined as functions of random variables or probabilisticvariables. For example, the decision variables B_(main,i) and B_(cap,i)can be defined as binary variables that have probabilistic values basedon the reliability of the building equipment. Low reliability values mayincrease the probability that the binary decision variables B_(main,i)and B_(cap,i) will have a value of one (e.g., B_(main,i)=1 andB_(cap,i)=1), whereas high reliability values may increase theprobability that the binary decision variables B_(main,i) and B_(cap,i)will have a value of zero (e.g., B_(main,i)=0 and B_(cap,i)=0). In someembodiments, step 1016 includes using a mixed integer stochastictechnique to define the values of the binary decision variablesB_(main,i) and B_(cap,i) as a probabilistic function of the reliabilityof the building equipment.

As discussed above, the objective function J may represent the predictedcost of operating, maintaining, and purchasing one or more devices ofthe building equipment over the duration of the optimization period. Insome embodiments, step 1016 includes projecting these costs back to aparticular point in time (e.g., the current time) to determine the netpresent value (NPV) of the one or more devices of the building equipmentat a particular point in time. For example, step 1016 can includeprojecting each of the costs in objective function J back to the currenttime using the following equation:

${NPV}_{cost} = {\sum\limits_{i - 1}^{h}\frac{{Cost}_{i}}{\left( {1 + r} \right)^{i}}}$where r is the interest rate, Cost_(i) is the cost incurred during timestep i of the optimization period, and NPV_(cost) is the net presentvalue (i.e., the present cost) of the total costs incurred over theduration of the optimization period. In some embodiments, step 1016includes optimizing the net present value NPV_(cost) to determine theNPV of the building equipment at a particular point in time.

As discussed above, one or more variables or parameters in the objectivefunction J can be updated dynamically based on closed-loop feedback fromthe building equipment. For example, the equipment performanceinformation received from the building equipment can be used to updatethe reliability and/or the efficiency of the building equipment. Step1016 can include optimizing the objective function J periodically (e.g.,once per day, once per week, once per month, etc.) to dynamically updatethe predicted cost and/or the net present value NPV_(cost) based on theclosed-loop feedback from the building equipment.

In some embodiments, step 1016 include generating optimization results.The optimization results may include the optimal values of the decisionvariables in the objective function J for each time step i in theoptimization period. The optimization results include operatingdecisions, equipment maintenance decisions, and/or equipment purchasedecisions for each device of the building equipment. In someembodiments, the optimization results optimize the economic value ofoperating, maintaining, and purchasing the building equipment over theduration of the optimization period. In some embodiments, theoptimization results optimize the net present value of one or moredevices of the building equipment at a particular point in time. Theoptimization results may cause BMS 606 to activate, deactivate, oradjust a setpoint for the building equipment in order to achieve theoptimal values of the decision variables specified in the optimizationresults.

In some embodiments, process 1000 includes using the optimizationresults to generate equipment purchase and maintenance recommendations.The equipment purchase and maintenance recommendations may be based onthe optimal values for the binary decision variables B_(main,i) andB_(cap,i) determined by optimizing the objective function J. Forexample, a value of B_(main,25)=1 for a particular device of thebuilding equipment may indicate that maintenance should be performed onthat device at the 25^(th) time step of the optimization period, whereasa value of B_(main,25)=0 may indicate that the maintenance should not beperformed at that time step. Similarly, a value of B_(cap,25)=1 mayindicate that a new device of the building equipment should be purchasedat the 25^(th) time step of the optimization period, whereas a value ofB_(cap,25)=0 may indicate that the new device should not be purchased atthat time step.

In some embodiments, the equipment purchase and maintenancerecommendations are provided to building 10 (e.g., to BMS 606) and/or toclient devices 448. An operator or building owner can use the equipmentpurchase and maintenance recommendations to assess the costs andbenefits of performing maintenance and purchasing new devices. In someembodiments, the equipment purchase and maintenance recommendations areprovided to service technicians 620. Service technicians 620 can use theequipment purchase and maintenance recommendations to determine whencustomers should be contacted to perform service or replace equipment.

Still referring to FIG. 10 , process 1000 is shown to include updatingthe efficiency and the reliability of the building equipment based onthe optimal maintenance strategy (step 1018). In some embodiments, step1018 includes updating the efficiency η_(i) for one or more time stepsduring the optimization period to account for increases in theefficiency η of the building equipment that will result from performingmaintenance on the building equipment or purchasing new equipment toreplace or supplement one or more devices of the building equipment. Thetime steps i at which the efficiency η_(i) is updated may correspond tothe predicted time steps at which the maintenance will be performed orthe equipment will replaced. The predicted time steps at whichmaintenance will be performed on the building equipment may be definedby the values of the binary decision variables B_(main,i) in theobjective function J. Similarly, the predicted time steps at which thebuilding equipment will be replaced may be defined by the values of thebinary decision variables B_(cap,i) in the objective function J.

Step 1018 can include resetting the efficiency η_(i) for a given timestep i if the binary decision variables B_(main,i) and B_(cap,i)indicate that maintenance will be performed at that time step and/or newequipment will be purchased at that time step (i.e., B_(main,i)=1 and/orB_(cap,i)=1). For example, if B_(main,i)=1, step 1018 can includeresetting the value of η_(i) to η_(main), where η_(main) is theefficiency value that is expected to result from the maintenanceperformed at time step i. Similarly, if B_(cap,i)=1, step 1018 caninclude resetting the value of η_(i) to η_(cap), where η_(cap) is theefficiency value that is expected to result from purchasing a new deviceto supplement or replace one or more devices of the building equipmentperformed at time step i. Step 1018 can include resetting the efficiencyη_(i) for one or more time steps while the optimization is beingperformed (e.g., with each iteration of the optimization) based on thevalues of binary decision variables B_(main,i) and B_(cap,i).

Step 1018 may include determining the amount of time Δt_(main,i) thathas elapsed since maintenance was last performed on the buildingequipment based on the values of the binary decision variablesB_(main,i). For each time step i, step 1018 can examine thecorresponding values of B_(main) at time step i and each previous timestep (e.g., time steps i−1, i−2, . . . , 1). Step 1018 can includecalculating the value of Δt_(main,i) by subtracting the time at whichmaintenance was last performed (i.e., the most recent time at whichB_(main,i)=1) from the time associated with time step i. A long amountof time Δt_(main,i) since maintenance was last performed may result in alower reliability, whereas a short amount of time since maintenance waslast performed may result in a higher reliability.

Similarly, step 1018 may include determining the amount of timeΔt_(cap,i) that has elapsed since the building equipment were purchasedor installed based on the values of the binary decision variablesB_(cap,i). For each time step i, step 1018 can examine the correspondingvalues of B_(cap) at time step i and each previous time step (e.g., timesteps i−1, i−2, . . . , 1). Step 1018 can include calculating the valueof Δt_(cap,i) by subtracting the time at which the building equipmentwere purchased or installed (i.e., the most recent time at whichB_(cap,i)=1) from the time associated with time step i. A long amount oftime Δt_(cap,i) since the building equipment were purchased or installedmay result in a lower reliability, whereas a short amount of time sincethe building equipment were purchased or installed may result in ahigher reliability

Some maintenance activities may be more expensive than other. However,different types of maintenance activities may result in different levelsof improvement to the efficiency η and/or the reliability of thebuilding equipment. For example, merely changing the oil in a chillermay result in a minor improvement in efficiency η and/or a minorimprovement in reliability, whereas completely disassembling the chillerand cleaning all of the chilled water tubes may result in asignificantly greater improvement to the efficiency η and/or thereliability of the building equipment. Accordingly, multiple differentlevels of post-maintenance efficiency (i.e., η_(main)) andpost-maintenance reliability (i.e., Reliability_(main)) may exist. Eachlevel of η_(main) and Reliability_(main) may correspond to a differenttype of maintenance activity.

In some embodiments, step 1018 includes identifying the maintenanceactivity associated with each binary decision variable B_(main,j,i) andresets the efficiency η to the corresponding post-maintenance efficiencylevel η_(main,j) if B_(main,j,i)=1. Similarly, step 1018 may includeidentifying the maintenance activity associated with each binarydecision variable B_(main,j,i) and can reset the reliability to thecorresponding post-maintenance reliability level Reliability_(main,j) ifB_(main,j,i)=1.

Some capital purchases may be more expensive than other. However,different types of capital purchases may result in different levels ofimprovement to the efficiency η and/or the reliability of the buildingequipment. For example, purchasing a new sensor to replace an existingsensor may result in a minor improvement in efficiency η and/or a minorimprovement in reliability, whereas purchasing a new chiller and controlsystem may result in a significantly greater improvement to theefficiency η and/or the reliability of the building equipment.Accordingly, multiple different levels of post-purchase efficiency(i.e., η_(cap)) and post-purchase reliability (i.e., Reliability_(cap))may exist. Each level of η_(cap) and Reliability_(cap) may correspond toa different type of capital purchase.

In some embodiments, step 1018 includes identifying the capital purchaseassociated with each binary decision variable B_(main,k,i) and resettingthe efficiency η to the corresponding post-purchase efficiency levelη_(cap,k) if B_(cap,k,i)=1. Similarly, step 1018 may include identifyingthe capital purchase associated with each binary decision variableB_(cap,k,i) and can resetting the reliability to the correspondingpost-purchase reliability level Reliability_(cap,k) ifB _(main,k,i)=1.Model Predictive Maintenance with Financial Analysis Functionality

Overview

Referring generally to FIGS. 11-14 , systems and methods for a modelpredictive maintenance (MPM) system with financial analysisfunctionality are shown, according to some embodiments. Integratingfinancial analysis into the MPM system can ensure that optimizationsaccount for a time value of money rather than only advertised costs. Asdescribed herein, costs can refer to any literal cost at a particulartime step whereas a value of money can be used to determine how much acost is worth in terms of a baseline value of money (e.g., a value ofmoney at a current time). The time value of money can refer to how avalue of money can change over time. For example, if a 5% interest rateis estimated over a next year, $1.00 at a current time can be worth theequivalent of $1.05 at the next year due to a decrease in value ofmoney. The value of money can increase/decrease for a variety of reasonssuch as, for example, changing federal interest rates,inflation/deflation, etc. As described herein, interest rates are usedto refer generally to various reasons for changes in the value of money.In some embodiments, interest rates are used to refer to one or morespecific reasons for changes in the value of money. In some embodiments,interest rates are used to refer to an aggregate of all changes in thevalue of money.

If the time value of money is not accounted for if optimizing anobjective function (e.g., the objective function J), decisions madebased on the optimization may be inaccurate. For example, consider asituation where a current cost of replacing a chiller unit is $1,000, acost of replacing the chiller unit in a year is $1,030, and a currentinterest rate is 5%. If the interest rate (i.e., the time value ofmoney) is not accounted for, it may be determined that replacing thechiller unit at a current time is more cost-effective than replacing thechiller unit next year as $1,000 is less than $1,030. However, byincorporating the interest rate, it can be determined that an adjustedcost of replacing the chiller unit next year is more cost-effective thanreplacing the chiller unit at the current time (assuming constantoperational costs). In particular, an adjusted cost of replacing thechiller unit next year can be determined to be approximately $981 interms of a current value of money. As such, accounting for the interestrate can be beneficial for determining how to optimally maintain andreplace building equipment over time.

MPM System with Financial Analysis

Referring now to FIG. 11 , MPM system 602 of FIG. 8 is shown in greaterdetail, according to some embodiments. In particular, high leveloptimizer 832 is shown to receive interest rates from an interest rateprovider 1102. Interest rate provider 1102 can be any service, system,controller, person, etc. that can provide interest rate values to MPMsystem 602. For example, interest rate provider 1102 may be a bankingservice that estimates interest rate values. In some embodiments,interest rate provider 1102 automatically provides interest rates to MPMsystem 602 as the interest rates are updated or provides the interestrates on a predetermined scheduled (e.g., every day). In someembodiments, MPM system 602 requests interest rates based on a need forthe interest rates. For example, MPM system 602 may send a request tointerest rate provider 1102 to provide the interest rates prior toperforming an optimization process. It should be appreciated that MPMsystem 602 can obtain values of the interest rate by other variousmethods depending on how interest rate provider 1102 operates. In someembodiments, interest rate provider 1102 is a component of MPM system602.

Based on the received interest rates, high level optimizer 832 canperform an optimization process to generate optimization results thataccount for interest rates over time. The optimization process performedby high level optimizer 832 is described in greater detail below withreference to FIG. 12 , however a brief explanation is provided here forclarity. As interest rates evolve over time, a value of money (oranother type of cost) can change. Particularly, assuming a positiveinterest rate, the value of money may decrease over time (i.e., a valueof an amount money at a current time is higher than the value of thesame amount of money at a future time). Due to changes in the value ofmoney, decisions included in the optimization results can be determinedbased on current year dollars (i.e., the current value of money) suchthat future values of money are adjusted to be reflective of the currentyear dollars.

In some embodiments, high level optimizer 832 uses a constant interestrate for each time step of a time period (e.g., an optimization period).Using the constant interest rate can simplify calculations, therebyresulting in processing savings. In some embodiments, high leveloptimizer 832 uses time-varying interest rates such that each time stepof the time period is associated with a specific interest rate. By usingtime-varying interest rates, results based on the optimization performedby high level optimizer 832 can be determined more accurately as changesin interest rates over time can be accounted for.

If interest rates are positive, high level optimizer 832 can multiplyall future costs by a factor between zero and one based on a value ofthe interest rate. In some embodiments, as described above, the interestrate utilized by high level optimizer 832 is a constant rate over theoptimization period. In some embodiments, the interest rate varies overtime such that an interest rate at a first time step of the optimizationperiod may be different than an interest rate at a second time step. Inany case, a factor including the interest rate can be calculated foreach time step of an optimization period and multiplied by a total costof maintenance, replacement, operations, and/or any other costs for eachtime step. Advantageously, the interest rate can be incorporated intothe optimization performed by high level optimizer 832 independent of anoptimization method used to perform the optimization.

By incorporating the interest rate, high level optimizer 832 cangenerate operational, maintenance, and replacement decisions forbuilding equipment that account for a time value of money. In this way,overall costs can be further optimized (e.g., reduced) for a user (e.g.,a building owner) as maintenance/replacement activities can be moreaccurately determined by accounting for a current value of costs atdifferent time steps of the optimization period.

Referring now to FIG. 12 , a block diagram further illustrating highlevel optimizer 832 of FIG. 9 is shown, according to some embodiments.As shown in FIG. 12 , high level optimizer 832 can incorporate interestrates in the objective function J and optimize the objective function Jbased on the interest rates.

High level optimizer 832 is shown to include an interest rate predictor1202 that can estimate interest rates and provide the estimated interestrates to objective function generator 935. Interest rate predictor 1202is shown to receive interest rate information. In some embodiments, theinterest rate information is included in information provided byinterest rate provider 1102 as described with reference to FIG. 11 . Theinterest rate information can include various information that interestrate predictor 1202 can use to estimate interest rates over anoptimization period. For example, the interest rate information mayinclude future interest rates. If the interest rate information includesfuture interest rates, interest rate predictor 1202 can directlygenerate and provide an interest rate term, discussed in greater detailbelow, to objective function generator 935. As another example, theinterest rate information may include values of past interest ratesindicating what the interest rates were at prior time steps. Based onthe past interest rates, interest rate predictor 1202 can estimatefuture interest rates. For example, if interest rates for a past threetime steps were 0.02, 0.03, and 0.04 respectively, interest ratepredictor 1202 may calculate an average of the past interest rates(i.e., 0.03) to include in the interest rate term provided to objectivefunction generator 935 for upcoming time steps of the optimizationperiod. In general, interest rate predictor 1202 can determine theinterest rates using a variety of estimation techniques.

The interest rate term provided by interest rate predictor 1202 can bedetermined based on estimated interest rates for future time steps ofthe optimization period. In some embodiments, the interest rate term hasthe following form:a _(k)=(1+r)^(−k)where a_(k) is the interest rate term for a time step k and r is aconstant interest rate for all time steps of the optimization period.a_(k) as shown above is calculated based on a constant value of r overthe optimization period. However, a time-varying interest rate can beused to calculate a_(k). Specifically, a_(k) with time-varying interestrates can be given by the following:

$a_{k} = {\frac{1}{1 + r_{1}} \times \frac{1}{1 + r_{2}} \times \ldots \times \frac{1}{1 + r_{k}}}$where r_(i) is an interest rate at a time step i such that i≤k. In thiscase, a_(k) can be provided for each time step during the optimizationperiod based on interest rates from a first time step through time stepk.

High level optimizer 832 is also shown to include a failure riskpredictor 1204. Failure risk predictor 1204 can generate a risk costterm and provide the risk cost term to objective function generator 935.As building equipment degrades over time, a probability of the buildingequipment failing may increase. Specifically, the probability that thebuilding equipment may fail at a future time step may be greater than orequal to the probability that the building equipment may fail at acurrent time step if no maintenance/replacement of the buildingequipment is performed. Failure of building equipment may require BMS606 to incur costs related to maintenance and/or replacement of thebuilding equipment along with various opportunity costs such as unmetloads or missed production. For example, if an indoor unit (IDU) of avariable refrigerant flow (VRF) system fails and the failure results ina safety hazard for occupants of a room, costs related to performingmaintenance/replacement of the IDU and costs related to closing the room(e.g., renting a new room for the occupants, cancelling meetings in theroom, missed production, etc.) may be incurred.

The risk cost term generated by failure risk predictor 1204 canincorporate a probability of failure of tracked building equipment fortime steps of an optimization period along with a cost of failure of thetracked building equipment. As described, the tracked building equipmentcan include any building equipment for which a degradation state and/orother performance information is observed.

Based on the risk cost term provided by failure risk predictor 1204,objective function generator 935 can generate an objective function(e.g., the objective function J) incorporating the risk cost term alongwith the cost terms provided by predictors 910-930. For example, theobjective function generated by objective function generator 935 mayhave the following form:

${J\left( m_{k} \right)} = {\sum\limits_{k = 1}^{h}\left\{ {{c_{{op},k}\left( \delta_{k} \right)} + {\begin{bmatrix}c_{{main},k} \\c_{{replace},k}\end{bmatrix}^{T}m_{k}} + {c_{{fail},k}^{T}{p_{{fail},k}\left( \delta_{k} \right)}}} \right\}}$where c_(op,k)(δ_(k)) is an operational cost dependent on a state ofdegradation δ_(k), c_(main,k) is a cost of maintenance at time step k ofan optimization period, c_(replace,k) is a cost of replacement at timestep k, m_(k) is a binary vector representing which maintenance actionsare taken at time step k, P_(fail,k) (δ_(k)) is a vector ofprobabilities of failure for each component of the tracked buildingequipment (e.g., each tracked component of BMS 606) dependent on thestate of degradation δ_(k), c_(fail,k) is a cost of failure of thetracked building equipment, and h is a total number of time steps of theoptimization period. In the above objective function, the T superscriptindicates a transpose of the associated matrix. Values of c_(fail,k) caninclude a cost to repair/replace the tracked building equipment and/orany opportunity costs related to failure of the tracked buildingequipment. It should be appreciated that the first block of themaintenance vector includes maintenance options while the second blockof the maintenance vector includes replacement options. The first andsecond blocks are split apart to illustrate how maintenance andreplacement of building equipment are both considered. In someembodiments, the first and second blocks indicating maintenance andreplacement options respectively are combined into a single block.Further, it should be appreciated that c_(fail,k) ^(T)p_(fail,k) (δ_(k))illustrates the risk cost term of the objective function.

In some embodiments, the objective function generated by objectivefunction generator 935 incorporating the risk cost term has thefollowing form:

$J = {{\sum\limits_{i = 1}^{h}{C_{{op},i}P_{{op},i}\Delta t}} + {\sum\limits_{i = 1}^{h}{C_{{main},i}B_{{main},i}}} + {\sum\limits_{i = 1}^{h}{C_{{cap},i}B_{{cap},i}}} + {\sum\limits_{i = 1}^{h}{c_{{fail},i}^{T}{p_{{fail},i}\left( \delta_{i} \right)}}}}$where c_(fail,i) is a cost of failure of building equipment at a timestep i of an optimization period, p_(fail,i) (δ_(i)) is a probability offailure at time step i based on a state of degradation δ_(i) at timestep i, and all other variables are as described above. Failure risk ofbuilding equipment is described in greater detail in U.S. patentapplication Ser. No. 16/457,314 filed Jun. 28, 2019, and in U.S. patentapplication Ser. No. 15/426,962 filed Feb. 7, 2017, the entiredisclosures of which are incorporated by reference herein.

Based on the objective function generated incorporating the risk costterm, the operational cost term, the maintenance cost term, and thecapital cost term, objective function generator 935 can incorporate theinterest rate term provided by interest rate predictor 1202. Forexample, the objective function J incorporating the interest rate termcan be shown by the following equation:

${J\left( m_{k} \right)} = {\sum\limits_{k = 1}^{h}{a_{k}\left\{ {{c_{{op},k}\left( \delta_{k} \right)} + {\begin{bmatrix}c_{{main},k} \\c_{{replace},k}\end{bmatrix}^{T}m_{k}} + {c_{{fail},k}^{T}{p_{{fail},k}\left( \delta_{k} \right)}}} \right\}}}$where a_(k) is given by the following equation:a _(k)=(1+r)^(−k)assuming a constant interest rate r. As described above, r can betime-varying such that a_(k) is given by the following equation:

$a_{k} = {\frac{1}{1 + r_{1}} \times \frac{1}{1 + r_{2}} \times \ldots \times \frac{1}{1 + r_{k}}}$Another example of the objective function J generated by objectivefunction generator 935 can be shown by the following equation:

$J = {{\sum\limits_{i - 1}^{h}{a_{i}\left( {C_{{op},i}P_{{op},i}\Delta t} \right)}} + {\sum\limits_{i - 1}^{h}{a_{i}\left( {C_{{main},i}B_{{main},i}} \right)}} + {\sum\limits_{i - 1}^{h}{a_{i}\left( {C_{{cap},i}B_{{cap},i}} \right)}} + {\sum\limits_{i - 1}^{h}{a_{i}\left( {c_{{fail},i}^{T}{p_{{fail},i}\left( \delta_{i} \right)}} \right)}}}$

By incorporating the interest rate term in the objective function J, atotal cost of operating, replacing, and maintaining the buildingequipment can be adjusted based on an interest rate at each time step kof the optimization period. As such, the optimization can be performedsuch that costs at future steps are adjusted to a value of money at apresent time step. In some embodiments, a time step other than thepresent time step is used as a baseline for a value of money to whichcosts for other time steps are adjusted to.

Based on the objective function including the risk cost term and theinterest rate term, objective function optimizer 940 can determineoptimal values of decision variables such that an overall cost isoptimized (e.g., minimized). Due to the risk cost term, certainmaintenance and/or replacement may occur at an earlier/later time stepthan if the risk cost term were not included in the objective function.Particularly, the risk cost term can be managed by objective functionoptimizer 940 such that a probability of failure for any building deviceof building equipment is kept sufficiently low such that costs areoptimized. The probability of failure of the building equipment can beestimated over a time period based on degradation models of the buildingequipment. The degradation models can define how the building equipmentis expected to degrade based on how the building equipment is operated.For example, a building device that is operating at a maximum load andin a high temperature space may degrade quicker than a building deviceoperated at a low load and cooler temperatures. In some embodiments,degradation models of building equipment are provided duringinstallation of the building equipment. In some embodiments, degradationmodels of the building equipment are generated by MPM system 602 basedon measured performance variables of the building equipment over time.

In some embodiments, the risk cost term requires objective functionoptimizer 940 to ensure building devices of building equipment havemaintenance/replacement performed more frequently than if the risk costterm were not included in the objective function such that degradationstates of the building devices do not reach critical levels where thebuilding devices are likely to fail.

In some embodiments, failure of building equipment is considered tooccur if a value of δ_(i) exceeds a randomly distributed thresholdvalue. In some embodiments, the threshold values of failure for eachbuilding device of building equipment differ depending on the specificbuilding device. For example, if degradation is measured as a percentageof reliability as compared to reliability at installation, a specificIDU may be considered to have failed if the specific IDU falls below 30%of installation reliability, whereas a fan of an HVAC system may beconsidered to have failed if the fan falls below 20% of installationreliability. In some embodiments, the threshold value of failure foreach building device of building equipment is the same. For example, ifdegradation is measured based on a percentage of installationreliability, if any building device falls below 15% of installationreliability, the building device may be considered to have failed. Insome embodiments, failure of building equipment is considered to occurif, for example, the building equipment cannot start, the buildingequipment is producing outputs that are dangerous for occupants (e.g.,smoke, harmful gasses, etc.). Other metrics of failure can also be usedto determine if the building equipment has failed. As such, ifoptimizing the objective function, objective function optimizer 940 candetermine values of decisions variables that decrease a probability ofbuilding devices failing.

In some embodiments, objective function optimizer 940 allows somebuilding devices of building equipment to have a high probability offailure (e.g., >50%, >60%, etc.) in order to prioritizemaintenance/replacement of other building devices. For example, tooptimize costs, objective function optimizer 940 may determine values ofdecisions variables that result in a fan having a high probability offailure in order perform maintenance/replacement of a ventilation shaftat an earlier time step. The decision to temporarily allow the fan tohave the high probability of failure may a smaller impact on cost (e.g.,due to additional maintenance and/or opportunity costs) in comparison toif the ventilation shaft were to fail. As such, maintenance/replacementof the ventilation shaft may be prioritized over maintenance/replacementof the fan in order to further optimize (e.g., reduce) overall costs.

In some embodiments, the optimization performed by objective functionoptimizer 940 is constrained by a risk aversion value. A risk aversionvalue can be set by a user and/or the system to indicate a maximumallowable probability of failure for certain building devices. Forexample, a user may set a risk aversion value of 45% for buildingdevices with a failure cost greater than $500. Due to the risk aversionvalue, the optimization can determine an optimal maintenance andreplacement schedule such that any building device with an estimatedfailure cost greater than $500 has a probability of failure of less than45% throughout an optimization period. Effectively, a risk aversionvalue can place a constraint on the optimization such that decisionvariables related to maintenance and/or replacement of buildingequipment ensure probability of failure of certain building devices iskept below a particular value. In some embodiments, if objectivefunction optimizer 940 cannot determine a solution that maintains aprobability of failure of a particular building device below a riskaversion value, an alert is provided to a user indicating theprobability of failure of the particular building device may exceed therisk aversion value.

In some embodiments, a probability of failure at any week into thefuture is found by integrating a density function from the beginning ofa week to the end of the week. The probability of failure can bemultiplied by a cost of failure and added to the cost function (e.g.,the objective function J). In some embodiments, the cost of failure is arandom variable rather than a fixed variable. In some embodiments, theprobability of failure is displayed on a device (e.g., a mobile device,a computer, etc.). For example, a cumulative distribution function (CDF)of the probability of failure can be indicated on the device as agradient indicating a probability of failure. The gradient may, forexample, transition from green to yellow to red such that greenindicates a probability of failure is low, yellow indicates failure islikely approaching, and red indicates failure is likely to happen in thenear future.

Due to the interest rate term, decision variables set by objectivefunction optimizer 940 can be determined such that costs are adjustedfor each time step into the future. As a result, somemaintenance/replacement activities may be determined to be optimal atdifferent time steps due to the value of money changing over time. Forexample, consider a situation where a cost of performing maintenance onan outdoor unit (ODU) of a VRF system is constant throughout anoptimization period by a maintenance provider (i.e., the maintenanceprovider does not change a cost of the maintenance throughout theoptimization period). If a positive interest rate exists, the value ofmoney may decrease over time from a current time step. As such, in termsof a present value of money, performing the maintenance of the ODU at afuture time step may be less expensive than performing the maintenanceat the current time step due to the value of money decreasing while thecost of the maintenance is constant. Alternatively, as another example,if the maintenance provider does adjust the cost of maintenance inaccordance with interest rates, a value of the maintenance may be thesame at both the current time step and the future time step. Withoutaccounting for the interest rates, the cost increase can appear toincrease a value of the maintenance, even though in reality the value isconstant when adjusted to a present value of money. As should beevident, the interest rate can impact decisions of the optimizationperformed by objective function optimizer 940.

Referring now to FIG. 13 , a graph 1300 illustrating differences in atotal predicted cost of performing a maintenance activity on buildingequipment due to an interest rate is shown, according to someembodiments. While graph 1300 is shown specific to a maintenanceactivity, it should be appreciated that interest rates for otheractivities (e.g., operational activities, replacement activities, etc.)can be approached similar to and/or the same as discussed below. Asshown by graph 1300, a first time step can represent a current time stepfor which a value of money in future time steps can be calculated basedon if accounting for an interest rate. At the first time step, anadjusted cost 1302 and a non-adjusted cost 1304 are shown to beequivalent. Adjusted cost 1302 can represent a cost of performing themaintenance activity that is adjusted based on an interest rate overtime whereas non-adjusted cost 1304 can represent a cost of performingthe maintenance that is not adjusted based on the interest rate.Adjusted cost 1302 and a non-adjusted cost 1304 may be equivalent at thefirst time step as an interest rate at the current time step may be 0.In other words, adjusted cost 1302 and non-adjusted cost 1304 can beequivalent at the first time step as a value of the cost of themaintenance activity in terms of a current value of money is equivalentdue to the interest rate equaling 0.

As shown by graph 1300, adjusted cost 1302 and non-adjusted cost 1304begin to diverge starting at a second time step. At the second time step(and throughout all future time steps shown in graph 1300), non-adjustedcost 1304 maintains a constant cost value. Non-adjusted cost 1304 canmaintain the constant cost value as a cost of the maintenance may notchange over time. For example, the maintenance activity may cost $1,000at every step during the optimization period. However, adjusted cost1302 can begin to decrease starting at the second time step byaccounting for an interest rate over time. Specifically, graph 1300 canrepresent a positive interest rate at all time steps such that the valueof money decreases over time. By accounting for the interest rate,adjusted cost 1302 can decrease as based on the value of money at thefirst time step. In other words, values of non-adjusted cost 1304 canreflect a literal cost of the maintenance activity at each time stepwhereas adjusted cost 1302 can reflect a cost of the maintenanceactivity based on the value of money at the first time step. As such,adjusted cost 1302 can indicate actual values of the maintenanceactivity that should be used if performing an optimization of anobjective function (e.g., the objective function J). It should beappreciated that graph 1300 may not be drawn to scale depending onvalues of the interest rate over time.

MPM Process with Financial Analysis

Referring now to FIG. 14 , a process 1400 for generating an optimalmaintenance and replacement strategy for building equipment thataccounts for interest rates is shown, according to some embodiments. Insome embodiments, certain steps of process 1400 are similar to and/orthe same as certain steps of process 1000 as described with reference toFIG. 10 . By accounting for the interest rates, decisions that furtheroptimize (e.g., minimize) costs over an optimization can be obtained.Accounting for the interest rates can ensure any decisions generated asa result of performing the optimization account for a time value ofmoney. In this way, changes in the value of money can be accounted forsuch that all costs are calculated reflective of a current value ofmoney regardless of what time step during an optimization period saidcosts may occur during. In some embodiments, a different baseline valueof money other than the current value of money is used to calculatecosts based on. In some embodiments, some and/or all steps of process1400 are performed by MPM system 602.

Process 1400 is shown to include operating building equipment to affecta variable state or condition in a building (step 1402). In someembodiments, steps 1402-1414 are similar to and/or the same as steps1002-1014 of process 1000 as described with reference to FIG. 10 . Insome embodiments, steps 1402-1414 are performed by MPM system 602.

Process 1400 is shown to defining a cost Cost_(risk) associated with afailure risk of the building equipment over the optimization period as afunction of the estimated reliability (step 1416). Cost_(risk) can bedefined by a total of all risk costs C_(risk,k) for each time step k ofan optimization period. In some embodiments, step 1416 includes usingthe estimated reliability of the building equipment over theoptimization period to determine a probability of failure of devices ofthe building equipment at each time step of the optimization period. Theprobability of failure can be determined based on a degradation model ofthe building equipment. The degradation model can define the buildingequipment may degrade over time based on operating conditions of thebuilding equipment (e.g., a load of the building equipment, temperaturein a space where the building equipment operates, etc.). Based on theprobability of failure of devices, an impact of failure on total costsover the optimization can be estimated. To estimate the impact offailure on total costs, costs related to equipment failure can bedetermined. In particular, a cost to perform maintenance/replacement ofbuilding devices and/or opportunity costs related to failure of thebuilding devices can be determined. Opportunity costs can include anycosts beyond maintenance/replacement costs that are incurred due tofailure of a building device. For example, if a heater of an HVAC systemfails, a space where the heater is located may need to be temporarilyclosed down (e.g., for occupant safety). Closing the space may result incosts related to occupants renting other spaces, cancellation ofvaluable meetings, etc., all of which can result in additional costsand/or lost opportunities that can affect total costs of a buildingsystem over an optimization period.

Step 1416 can include determining the costs C_(risk,k) associated withvarious risk costs (e.g., a total of maintenance/replacement costs andopportunity costs) at a time step k. Based on the equipment performanceinformation and/or the estimated efficiency and reliability of buildingequipment determined/estimated in steps 1404 and 1406 respectively, astate of degradation can be estimated. As the estimated state ofdegradation increases, a probability of failure of building devices mayalso increase.

To estimate a state of degradation of all building devices, step 1416can include, for example, comparing a current estimated reliability ofeach building device and an optimal reliability based on when eachbuilding device was originally installed. To determine a value ofC_(risk,k), step 1416 can also include estimating a failure costassociated with each building device at each time step k. In someembodiments, failure cost of a building device is estimated by users. Insome embodiments, failure cost of a building device is estimated by asystem (e.g., MPM system 602) based on various information such as, forexample, a location of the building device, how the building deviceaffects conditions of a space, etc.

Based on the probability of failure and a failure cost of each buildingdevice for a time step k, C_(risk,k) can be determined by the followingequation:C _(risk,k) =c _(fail,k) ^(T) p _(fail,k)(δ_(k))where p_(fail,k)(δ_(k)) is a vector of probabilities of failure for eachbuilding device of the tracked building equipment on the state ofdegradation δ_(k), c_(fail,k) matrix defining a cost of failure of eachbuilding devices. Further, a value of Cost_(risk) (i.e., a total riskcost over an optimization period) can be determined by the followingequation:

${Cost}_{risk} = {\sum\limits_{i = 1}^{h}{c_{{fail},i}^{T}{p_{{fail},i}\left( \delta_{i} \right)}}}$where h is a total number of time steps in the optimization period. Insome embodiments, step 1416 is performed by failure risk predictor 1204.

Process 1400 is also shown to include estimating an interest rate ateach time step of the optimization period to define an interest rateterm a_(k) (step 1418). The interest rate at each time step can beestimated based on available interest rate information. The availableinterest rate information can include information such as estimatedfuture interest rates, historical interest rates, economic predictions,etc. Based on the available interest rate information, the interestrates can be estimated for each time step. In some embodiments, a singleinterest rate r is estimated and applied to each time step. In someembodiments, the interest rate is time-varying such during theoptimization period is associated with a specific interest rate value.

Based on the interest rate(s) determined, a_(k) can be determined foreach time step k. If the single interest rate r is used, a_(k) may havethe following form:a _(k)=(1+r)^(−k)

Alternatively, if the time-varying interest rate is determined for eachtime step k, a_(k) may have the following form:

$a_{k} = {\frac{1}{1 + r_{1}} \times \frac{1}{1 + r_{2}} \times \ldots \times \frac{1}{1 + r_{k}}}$In this way, a_(k) can define a factor to apply to costs relatedmaintenance, replacement, operational, and failure risk as to ensureeach cost is calculated in terms of a current value of money. In someembodiments, a different value of money rather than the current value ofmoney is used as a baseline to calculate adjusted costs.

Process 1400 is also shown to include optimizing an objective functionincluding the costs Cost_(op), Cost_(main), Cost_(risk), Cost_(cap), anda_(k) to determine an optimal maintenance and replacement strategy forthe building equipment (step 1420). In some embodiments, step 1420 issimilar to and/or the same as step 1016 of process 1000 as describedwith reference to FIG. 10 . The optimal maintenance and replacementstrategy can indicate optimal decisions related to maintaining and/orreplacing the building equipment over the optimization. By incorporatingCost_(risk) into the objective function, certain building devices of thebuilding equipment may be prioritized for maintenance/replacement toensure a probability of failure is kept low. To optimize (e.g., reduce)results of the objective function, building devices with a highopportunity cost associated with failure may be determined by theobjective function to receive additional and/or more frequentmaintenance/replacement to ensure a probability of failure of thebuilding devices with the high opportunity cost is kept low (e.g., 1%,5%, etc.).

In some embodiments, the optimization is constrained by a risk aversionvalue. A risk aversion value can be set by a user and/or the system toindicate a maximum allowable probability of failure for certain buildingdevices. For example, a user may set a risk aversion value of 20% forbuilding devices with a failure cost equal to or greater than $1,000.Due to the risk aversion value, the optimization can determine anoptimal maintenance and replacement schedule such that any buildingdevice with an estimated failure cost equal to or greater than $1,000has a probability of failure of less than 20% throughout an optimizationperiod. Effectively, a risk aversion value can place a constraint on theoptimization such that decision variables related to maintenance and/orreplacement of building equipment ensure probability of failure ofcertain building devices is kept below a particular value.

Further, by accounting for the interest rate over the optimizationperiod, costs at each time step can be adjusted to reflect a value ofmoney at a first time step of the optimization period. In this way,changes in the value of money should not affect decisions of theoptimization. In some embodiments, the objective function optimized instep 1420 has the following form:

${J\left( m_{k} \right)} = {\sum\limits_{k = 1}^{h}{a_{k}\left\{ {{c_{{op},k}\left( \delta_{k} \right)} + {\begin{bmatrix}c_{{main},k} \\c_{{replace},k}\end{bmatrix}^{T}m_{k}} + {c_{{fail},k}^{T}{p_{{fail},k}\left( \delta_{k} \right)}}} \right\}}}$where all variables are as defined above with reference to FIG. 12 . Inthis case, c_(op,k)(δ_(k)) over each time step k can define Cost_(op),

$\begin{bmatrix}c_{{main},k} \\c_{{replace},k}\end{bmatrix}^{T}$m_(k) over each time step k can define a combined Cost_(main) andCost_(cap), and c_(fail,k) ^(T)p_(fail,k)(δ_(k)) over each time step kcan define Cost_(risk). As shown in the above objective function, a_(k)can be applied to each cost for each time step k of the optimizationperiod. In this way, all costs are adjusted to be reflective of a valueof money at the first time step (i.e., time step k=1). In someembodiments, step 1420 is performed by objective function optimizer 940.

Process 1400 is shown to include updating the efficiency and reliabilityof the building equipment based on the optimal maintenance andreplacement strategy (step 1422). In some embodiments, step 1422 issimilar to and/or the same as step 1018 of process 1000 as describedwith reference to FIG. 10 . In some embodiments, step 1422 is performedby MPM system 602.

Configuration of Exemplary Embodiments

The construction and arrangement of the systems and methods as shown inthe various exemplary embodiments are illustrative only. Although only afew embodiments have been described in detail in this disclosure, manymodifications are possible (e.g., variations in sizes, dimensions,structures, shapes and proportions of the various elements, values ofparameters, mounting arrangements, use of materials, colors,orientations, etc.). For example, the position of elements can bereversed or otherwise varied and the nature or number of discreteelements or positions can be altered or varied. Accordingly, all suchmodifications are intended to be included within the scope of thepresent disclosure. The order or sequence of any process or method stepscan be varied or re-sequenced according to alternative embodiments.Other substitutions, modifications, changes, and omissions can be madein the design, operating conditions and arrangement of the exemplaryembodiments without departing from the scope of the present disclosure.

The present disclosure contemplates methods, systems and programproducts on any machine-readable media for accomplishing variousoperations. The embodiments of the present disclosure can be implementedusing existing computer processors, or by a special purpose computerprocessor for an appropriate system, incorporated for this or anotherpurpose, or by a hardwired system. Embodiments within the scope of thepresent disclosure include program products comprising machine-readablemedia for carrying or having machine-executable instructions or datastructures stored thereon. Such machine-readable media can be anyavailable media that can be accessed by a general purpose or specialpurpose computer or other machine with a processor. By way of example,such machine-readable media can comprise RAM, ROM, EPROM, EEPROM, CD-ROMor other optical disk storage, magnetic disk storage or other magneticstorage devices, or any other medium which can be used to carry or storedesired program code in the form of machine-executable instructions ordata structures and which can be accessed by a general purpose orspecial purpose computer or other machine with a processor. Combinationsof the above are also included within the scope of machine-readablemedia. Machine-executable instructions include, for example,instructions and data which cause a general purpose computer, specialpurpose computer, or special purpose processing machines to perform acertain function or group of functions.

Although the figures show a specific order of method steps, the order ofthe steps may differ from what is depicted. Also two or more steps canbe performed concurrently or with partial concurrence. Such variationwill depend on the software and hardware systems chosen and on designerchoice. All such variations are within the scope of the disclosure.Likewise, software implementations could be accomplished with standardprogramming techniques with rule based logic and other logic toaccomplish the various connection steps, processing steps, comparisonsteps and decision steps.

What is claimed is:
 1. A model predictive maintenance system forbuilding equipment, the system comprising: one or more processingcircuits comprising one or more processors and memory storinginstructions that, when executed by the one or more processors, causethe one or more processors to perform operations comprising: performingan optimization of an objective function that defines a present value ofa total cost comprising a first cost of operating the building equipmentand a second cost of performing maintenance on the building equipment asa function of operating decisions and maintenance decisions for thebuilding equipment for a plurality of time steps within a time period,the total cost comprising one or more costs incurred during one or morefuture time steps of the time period, wherein the objective functiondefines the present value of the total cost by reducing the one or morecosts incurred during the one or more future time steps based on one ormore amounts of time until the one or more future time steps occur,wherein the optimization determines a specific type of maintenanceactivity to be performed at a time step within the time period from aset of multiple different types of maintenance activities based on (1)values of the first cost of operating the building equipment predictedto result from performing the multiple different types of themaintenance activities at the time step and (2) values of the secondcost of performing maintenance on the building equipment predicted toresult from performing the multiple different types of the maintenanceactivities at the time step; and operating the building equipment andperforming maintenance on the building equipment in accordance withdecisions defined by a result of the optimization.
 2. The system ofclaim 1, wherein the objective function defines the present value byreducing the one or more costs incurred during the one or more futuretime steps further based on an interest rate.
 3. The system of claim 2,wherein the objective function accounts for variation in the interestrate over the time period.
 4. The system of claim 1, wherein theobjective function further defines a second present value of a totalcost of replacing the building equipment as a function of replacementdecisions for the building equipment for the plurality of time stepswithin the time period, the total cost of replacing the buildingequipment comprising a cost of replacing the building equipment incurredduring a future time step of the time period.
 5. The system of claim 1,wherein the objective function further defines a risk cost associatedwith a failure risk of the building equipment at the plurality of timesteps of the time period, the risk cost determined based on adegradation model of the building equipment.
 6. The system of claim 1,wherein the first cost of operating the building equipment is a functionof the maintenance decisions for the building equipment; and theoptimization is performed to minimize the net present value.
 7. Thesystem of claim 1, the operations further comprising updating thepresent value based on closed-loop feedback of the building equipment,the closed-loop feedback of the building equipment used to update atleast one of: an efficiency of the building equipment; or a reliabilityof the building equipment; wherein the optimization is performed basedon the efficiency of the building equipment and the reliability of thebuilding equipment.
 8. A method for performing model predictivemaintenance of building equipment, the method comprising: performing anoptimization of an objective function that defines a present value of atotal cost comprising a first cost of operating the building equipmentand a second cost of performing maintenance on the building equipment asa function of operating decisions and maintenance decisions for thebuilding equipment for a plurality of time steps within a time period,the total cost comprising one or more costs incurred during one or morefuture time steps of the time period, wherein the objective functiondefines the present value of the total cost by reducing the one or morecosts incurred during the one or more future time steps based on one ormore amounts of time until the one or more future time steps occur,wherein the optimization determines a specific type of maintenanceactivity to be performed at a time step within the time period from aset of multiple different types of maintenance activities based on (1)values of the first cost of operating the building equipment predictedto result from performing the multiple different types of themaintenance activities at the time step and (2) values of the secondcost of performing maintenance on the building equipment predicted toresult from performing the multiple different types of the maintenanceactivities at the time step; and operating the building equipment andperforming maintenance on the building equipment in accordance withdecisions defined by a result of the optimization.
 9. The method ofclaim 8, wherein the objective function defines the present value byreducing the one or more costs incurred during the one or more futuretime steps further based on an interest rate.
 10. The method of claim 9,wherein the objective function accounts for variation in the interestrate over the time period.
 11. The method of claim 8, wherein theobjective function further defines a second present value of a totalcost of replacing the building equipment as a function of replacementdecisions for the building equipment for the plurality of time stepswithin the time period, the total cost of replacing the buildingequipment comprising a cost of replacing the building equipment incurredduring a future time step of the time period.
 12. The method of claim 8,wherein the objective function further defines a risk cost associatedwith a failure risk of the building equipment at the plurality of timesteps of the time period, the risk cost determined based on adegradation model of the building equipment.
 13. The method of claim 8,wherein: the present value is a net present value of operating andmaintaining the building equipment over the time period; theoptimization is performed to minimize the net present value.
 14. Themethod of claim 8, further comprising updating the present value basedon closed-loop feedback of the building equipment, the closed-loopfeedback of the building equipment used to update at least one of: anefficiency of the building equipment; or a reliability of the buildingequipment; wherein the optimization is performed based on the efficiencyof the building equipment and the reliability of the building equipment.15. A controller for performing model predictive maintenance of buildingequipment, the controller comprising: one or more processors; and one ormore non-transitory computer-readable media storing instructions that,when executed by the one or more processors, cause the one or moreprocessors to perform operations comprising: performing an optimizationof an objective function that defines a present value of a total costcomprising a first cost of operating the building equipment and a secondcost of performing maintenance on the building equipment as a functionof operating decisions and maintenance decisions for the buildingequipment for a plurality of time steps within a time period, the totalcost comprising one or more costs incurred during one or more futuretime steps of the time period, wherein the objective function definesthe present value of the total cost by reducing the one or more costsincurred during the one or more future time steps based on one or moreamounts of time until the one or more future time steps occur, whereinthe optimization determines a specific type of maintenance activity tobe performed at a time step within the time period from a set ofmultiple different types of maintenance activities based on (1) valuesof the first cost of operating the building equipment predicted toresult from performing the multiple different types of the maintenanceactivities at the time step and (2) values of the second cost ofperforming maintenance on the building equipment predicted to resultfrom performing the multiple different types of the maintenanceactivities at the time step; and operating the building equipment andperforming maintenance on the building equipment in accordance withdecisions defined by a result of the optimization.
 16. The controller ofclaim 15, wherein the objective function defines the present value byreducing the one or more costs incurred during the one or more futuretime steps further based on an interest rate.
 17. The controller ofclaim 16, wherein the objective function accounts for variation of theinterest rate over the time period.
 18. The controller of claim 15,wherein the objective function further defines a second present value ofa total cost of replacing the building equipment as a function ofreplacement decisions for the building equipment for the plurality oftime steps within the time period, the total cost of replacing thebuilding equipment comprising a cost of replacing the building equipmentincurred during a future time step of the time period.
 19. Thecontroller of claim 15, wherein the objective function further defines arisk cost associated with a failure risk of the building equipment atthe plurality of time steps of the time period, the risk cost determinedbased on a degradation model of the building equipment.
 20. Thecontroller of claim 15, wherein: the present value is a net presentvalue of operating and maintaining the building equipment over the timeperiod; the optimization is performed to minimize the net present value.